Everton's Iliman Ndiaye scored a brilliant solo goal against Tottenham
Everton started the road to recovery under returning manager David Moyes and piled more pressure on his struggling Tottenham counterpart Ange Postecoglou with an impressive victory at Goodison Park.
Spurs were shambolic for long periods as they were overrun by a resurgent Everton, who had won only three Premier League matches this season - scoring 15 goals - before this game.
Everton deservedly led 3-0 at the interval, then survived a late Spurs revival as the scoreline was given an appearance that did not reflect the difference between the sides.
With the stakes high for both teams, Everton brushed Spurs aside in the opening period, building the platform for a win that condemned Postecoglou's men to a seventh defeat in their past 10 league games.
Dominic Calvert-Lewin ended a barren Premier League scoring sequence stretching back to September - and lasting 1,288 minutes - when he turned Archie Gray twice in the area before leaving Spurs keeper Antonin Kinsky wrong-footed with a smart finish.
Son Heung-min was denied twice by Jordan Pickford but it was Everton, unrecognisable from the goal-shy team seen previously this season, who added a second on the half-hour when Iliman Ndiaye twisted Radu Dragusin inside out before firing high past Kinsky.
Everton compounded Spurs' misery in first-half stoppage time when Gray turned into his own net after James Tarkowski's header took a touch off Calvert-Lewin.
Spurs, as they had to do, improved after the break and pulled a goal back through Dejan Kulusevski's clever lofted finish with 13 minutes left, with former Everton striker Richarlison increasing the nerves by bundling home in injury time.
But the hosts held out for a deserved win on a day to savour for the returning Moyes.
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Everton entered this game mired in pessimism and mediocrity and looking to the familiar figure of Moyes, who managed them for 11 years between 2002 and 2013, to be the catalyst for Premier League safety.
The 61-year-old Scot's first game ended in a home defeat by Aston Villa, but more time on the training ground with his new charges brought the first signs of hope for the rest of the campaign.
And symbolic of that was the performance of Calvert-Lewin, who has struggled for form and confidence this season, exemplified by missing three good opportunities against Villa.
Calvert-Lewin set Everton on their way with a smart finish, then led Everton's line with vigour and presence as Spurs were outfought in the physical exchanges.
Ndiaye has been a shining light this season and illuminated Goodison Park once more with a thrilling second goal, while changes made by Moyes to his starting line-up also did the trick.
Powerful Republic of Ireland defender Jake O'Brien made a solid Premier League debut having been marginalised by Dyche after his £20m summer move from Lyon, while Jesper Lindstrom played with a confidence and drive that had not been since his arrival on loan from Napoli.
There was still an air of anxiety around Goodison when Spurs did eventually show signs of life and threatened an unlikely late comeback, but otherwise this was the sort of performance Everton and their fans have been waiting for all season.
Spurs late show cannot disguise flaws
Spurs 'fallen short again' in Everton loss - Postecoglou
Tottenham and their manager were hugely flattered by losing by just one goal, and that margin cannot cover up the abysmal first 45 minutes during which this game was lost.
And while they are clinging to the possibilities offered by a one-goal advantage in the Carabao Cup semi-final second leg against Liverpool at Anfield, those hopes will be snuffed out very swiftly if they perform as badly as this.
Postecoglou is unquestionably struggling for resources, with striker Dominic Solanke the latest casualty with a knee injury, but there can be no excuses for a first half that understandably left the travelling fans in a fury, a fury mainly aimed at chairman Daniel Levy.
Spurs gave the score a respectable look with those goals from Kulusevski and Richarlison, but in reality it was a deception.
Everton have struggled to create goals and chances all season, yet they cut through Spurs with embarrassing ease in that first half, scoring three and having more chances.
The nerves kicked in when Spurs mounted their late rally, but the mediocrity of that first 45 minutes cost them dearly and will turn an even more unforgiving spotlight on Postecoglou.
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