The Welshman produced a dynamic performance on Spurs' right flank, but twice drifted inside to finish calmly past Aaron Ramsdale.
Johnson, who looked a little annoyed that Mathys Tel took the penalty he won in second half stoppage time, was deservedly named player of the match.
With 11 goals and three assists this term, Johnson's second season at Spurs is set to surpass his first.
He's Spurs' top scorer this season in the Premier League this season, something not many would have expected with Son Heung-min and Dominic Solanke in the same side.
Now that he has hit double figures for league goals for the third time in his career, Johnson should go into next season as one of Spurs' key players.
'We looked threatening every time we went forward'published at 16:26 6 April
16:26 6 April
Image source, Getty Images
Tottenham manager Ange Postecoglou has been speaking to Sky Sports following the win: "The first half was really good, I'm really pleased. We were a bit sloppy with the ball in the second half. There's stuff to improve on but it's a victory with three goals, so it's positive. We looked threatening every time we went forward in the first half."
On Brennan Johnson's performance: "You want as many players in good form. Brennan is always a threat whenever he plays. He was really good today. He is always a goal threat."
On having a goal disallowed for offside: "Once again, we are waiting around for six or seven minutes at a football game which would have been unheard of a few years ago."
Tottenham 3-1 Southampton: Key statspublished at 16:18 6 April
16:18 6 April
Image source, Getty Images
Brennan Johnson (15th and 16th today) is the first Tottenham Hotspur player to score 15+ goals in all competitions in a season, other than Harry Kane or Son Heung-min, since Gareth Bale in 2020-21 (also 16).
Mathys Tel (19y 344d) is the first teenager to score for Tottenham Hotspur in the Premier League since Dele Alli in April 2016 (19y 365d vs Manchester United) and the second Spurs teen to score a penalty in the competition after Nick Barmby in December 1993 (19y 296 vs Newcastle).
Tottenham 3-1 Southampton- send us your thoughtspublished at 16:01 6 April
Sutton's predictions: Tottenham v Southamptonpublished at 11:14 6 April
11:14 6 April
It was almost a big week for Southampton, who would have surpassed the Premier League's record-lowest points total, currently held by Robbie Savage's Derby County, if they had held on to beat Crystal Palace on Wednesday.
They came agonisingly close and in many ways I would take a Saints victory here, just so I can enjoy hosting 606 with Robbie between now and the end of the season.
You will probably all have heard him recently, banging on about what a job he has done to take big-budget Macclesfield to promotion from the Northern Premier League, but I'd like to balance things a little bit with him hanging on to his record.
I can't see Southampton taking three points here, though, even if the two other teams in the bottom three have already gone to Tottenham and won.
Spurs won 5-0 at St Mary's before Christmas, in Russell Martin's final game as Saints boss.
Ange Postecoglou's side are not playing well, so they won't score as many this time, but it should still be very comfortable for them and they might even keep a clean sheet.
Would winning the Europa League change anything at Spurs?published at 12:05 5 April
12:05 5 April
Media caption,
Ange Postecoglou faced more criticism from some Tottenham fans after their 1-0 defeat by Chelsea in the Premier League but would winning the Europa League this season change his standing at the club?
Former Spurs midfielder Michael Brown tells The Football News Show why the club must stick with him until the end of the season at least but warns even silverware might only paper over the cracks at Tottenham Hotspur Stadium.
Tottenham v Southampton: Did you know?published at 15:58 4 April
15:58 4 April
Image source, Getty Images
Southampton have won just one of their past seven Premier League games against Tottenham, beating them 3-2 at Tottenham Hotspur Stadium in February 2022.
None of Tottenham's past 15 Premier League home games against Southampton have finished level (W12 L3). Tottenham have scored in all of those games, while the Saints have also found the net in each of the past eight games.
Son Heung-min has had a hand in 18 goals in 16 Premier League appearances against Southampton (11 goals, seven assists). The only current Premier League player with more goals and assists against a single opponent is Mohamed Salah against Manchester United (13 goals, six assists).
Postecoglou on dealing with criticism, VAR and Van de Venpublished at 12:09 4 April
12:09 4 April
Millie Sian BBC Sport journalist
Tottenham boss Ange Postecoglou has been speaking to the media before Sunday's Premier League game against Southampton (kick-off 14:00 BST).
Here are the key lines from his news conference:
There hasn't been a lot of time to reflect on the 1-0 defeat to Chelsea on Thursday night but he intends to do that in training today.
He said that Tottenham have taken their "fair share of blows this season" but the aim is to "dust themselves off" and "work on repeating a lot of what they showed" against Chelsea last time out.
He said he doesn't "get affected" by any negativity or criticism he receives from the supporters, but "it is a little bit unfair to target the players in this situation".
When asked about cupping his ear towards the Tottenham supporters after Pape Matar Sarr's disallowed goal, he responded: "I made a mistake, I celebrated a goal. Since VAR came in, I've made a conscious effort to not really celebrate goals anymore because you have to wait for everything to get checked off."
He was keen to highlight that his response was to "celebrate and get the fans to make some noise" after the goal, adding: "My mistake was celebrating a goal - VAR has defeated me - so I won't be doing that again."
His comment about feeling "such a disconnect with the world" was in relation to VAR: "As human beings, we are just so accepting of everything. We accepted mobile phones into our lives and now we are trying to reel them back because of the damage they cause. It's too late - the horse is bolted - and it is the same with VAR in football, but we just let it roll on."
Micky van de Ven "cramped up" last time out but there is no further injury concern: "He hasn't played for 90 minutes for a while, but the positive thing is that he felt good apart from that. It was a tough game defensively, so he had to work hard."
Dane Scarlett was left out of the squad due to being "a bit sore" after coming back from a loan spell where he had not played much. He was given the weekend off but has been "working really hard in training to get his conditioning up".
Southampton's visit to Tottenham Hotspur Stadium will be an opportunity to "build some momentum" going into their Europa League quarter-final first leg against Eintracht Frankfurt on Thursday.
There will be a couple of changes and he will rotate his squad "to a certain extent", but the players are "in a good place physically" so he doesn't feel the need to manage their game time.
'Toothless, passive, hopeless, clueless'published at 08:42 4 April
08:42 4 April
Image source, Getty Images
We asked for your views on Chelsea's win over Tottenham in the Premier League.
Here are some of your comments:
GT: Toothless, passive, hopeless, clueless - take your pick. Ange has no excuse because we have all of our players back. That was shocking.
James: Our style of play under Ange has been so laborious, sloppy and littered with mistakes. We put up a reasonable effort but you would normally look to a manager to instil more discipline in how we play. Antonio Conte used to drill the side and we got results. That's what is missing. I'm looking forward to the summer and hopefully a new manager. Until then, we suffer.
Joshua: Yet another miserable performance. We only showed signs of threat near the end of the game, by which time it was too late. Ange is hanging by his last thread - the Europa League. If he doesn't win that 'trophy in his second year', then I don't see him having a future at Spurs. It was great at the start, but now Ange's reign has to come to an end if we want to improve as a football team.
Andy: Poor Ange has been out of his depth all season. He is a one-trick pony and the best managers in the world have worked him out quickly. The players look dispirited. We have no chance of winning another game in Europe and even the Southampton game is a worrying fixture.
Dave: The table doesn't lie - 16 games lost. We are wholly incompetent and clueless, on and off the pitch.
Jack: There's nothing to commend, no desire and no intensity. It's just horrible to watch. Massive changes are required at the club over the summer, but they won't happen. The club is in decline on the football side, and it means nothing to the fans that they are doing well financially.
Postecoglou 'looking more isolated than ever'published at 08:05 4 April
08:05 4 April
Nizaar Kinsella BBC Sport football news reporter
Image source, Getty Images
Tottenham head coach Ange Postecoglou is looking more isolated than ever.
The Australian directed a brief clap towards the furious travelling away fans from near the halfway line following his side's 1-0 loss at Chelsea but, by then, it could be argued the damage had already been done.
Chants of "you don't know what you're doing" came from the away end after midfielder Lucas Bergvall was replaced by Pape Sarr in the 65th minute.
Remarkably, Sarr found the net with an excellent long-range strike just four minutes later, leading Postecoglou to cup his ear and turn to the away end, only for VAR to then rule out the goal for a foul on Moises Caicedo.
Reports suggest Postecoglou is under severe pressure. Bournemouth's Andoni Iraola, Fulham's Marco Silva and Brentford's Thomas Frank have all been linked with his job.
The 56-year-old, who became Spurs boss in June 2023 and is contracted to the club until 2027, even suggested in midweek, external there were plenty of outstanding candidates, to replace him.
However, Spurs are expected to at least wait until the culmination of the Europa League campaign - a chance not only to win a first trophy in 17 years, but also to qualify for next season's Champions League.
Jamie Redknapp, speaking to Sky Sports, said after the match: "I think for Ange Postecoglou, it feels like he's going to make history or be history.
"When you lose 16 games in a season as Tottenham manager, still having great players at your disposal, it's not going to wash with the fans."
Like Postecoglou, chairman and co-owner Daniel Levy has faced criticism from the fans.
But Levy has given the head coach resources to shape a squad - Postecoglou has spent £214.8m.
That extra spend was an attempt to salvage the season while alive in three cup competitions, but after elimination from the domestic cups, it is Europa League or bust.
With little to play for in the Premier League, a end to the Spurs trophy drought would end the season on a high.
'I am at some disconnect with the world these days' - Postecogloupublished at 07:47 4 April
07:47 4 April
Image source, Getty Images
Tottenham boss Ange Postecoglou, speaking to Sky Sports after Thursday's 1-0 defeat at Stamford Bridge: "A difficult night, a tight game and not an easy place to come. We had to work hard to stay in the game. We let in a disappointing goal then fought our way back into the game but weren't able to get anything out of it.
"It is still a work in progress. In the final third, we could've been a bit cleaner with our football but for the most part we handled it quite well.
"It's a tough ask coming here, there was still enough there tonight to show the lads are getting back to the level we need."
On the intervention of VAR after it ruled out a Pape Matar Sarr equaliser: "It's killing the game mate, it's not the same game it used to be.
"You are standing around for 12 minutes. It's just killing the game, but no-one cares about that - they just love the drama and controversy and I'm sure there will be 24 hours' discussion about it and that's what everyone wants. They're not really interested that it's killing the spectacle of the game.
"If a referee sees that and he needs to see it for six minutes, what's clear and obvious about it?"
On claims he cupped his ears towards Spurs fans: "Oh, jeez mate. It is incredible. We just scored - I wanted to hear them cheer, I wanted them to get excited. I wanted to win the game with the momentum - it wasn't the first time my substitution was booed.
"I am at some disconnect with the world these days - I don't know. Maybe you are right."
Did you know?
Only the Premier League's current bottom four teams have lost more games this season than Tottenham, with Spurs losing 16 league games in a campaign for the first time since 2003-04 under Glenn Hoddle and David Pleat (19).
Tottenham have failed to win any of their past nine Premier League games against teams starting the day in the top half of the table (drawn one, lost eight).
Gossip: Tottenham want to keep Kulusevskipublished at 07:27 4 April
07:27 4 April
Tottenham hope to avoid losing 24-year-old midfielder Dejan Kulusevski this summer, amid interest from AC Milan and Napoli. (GiveMeSport), external
Chelsea 1-0 Tottenham: Pressure mounts for Postecogloupublished at 00:11 4 April
00:11 4 April
Emily Salley BBC Sport journalist
Image source, Getty Images
The unwanted stats and records keep mounting up for Ange Postecoglou.
And the the fans seem to turning against him, too, with sections of the away support at Stamford Bridge singing "you don't know what you're doing".
The defeat saw Postecoglou become the first Spurs manager ever to lose each of his first four league encounters with Chelsea.
The result leaves Tottenham a significant 10 points off the top 10, a whopping 39 points behind leaders Liverpool and just 14 points above the relegation zone.
On course to finish in the bottom half of the table for the first time in 17 years, Spurs are also at risk of matching their worst ever Premier League finish - when they finished 15th under manager Ossie Ardiles in 1994.
This Premier League season looks to be a lost cause for Spurs and Postecoglou's future at the club now seems to rely heavily on success in the Europa League.