Abdoulaye Doucoure scored his first goal of the season for Everton
Goalkeeper Alex McCarthy was the hero in the penalty shootout, saving Ashley Young's penalty in sudden death, as Southampton edged past Everton to reach the fourth round of the Carabao Cup.
In a battle of the Premier League’s two sides yet to pick up a point, the match went to a shootout after a 1-1 draw in normal time.
The first 11 efforts all found the back of the net, but Young’s strike was saved by McCarthy, leaving the travelling Southampton fans with a joyous long trip back to the south coast.
"I am really proud of the players," said Saints boss Russell Martin. "I understand what we are asking them to do is so tough but they do it with so much courage, conviction and intensity.
"I am really happy, we responded brilliantly to a setback. They stuck at it, puffed their chests out and were aggressive. I saw a lot of stuff that I liked."
Captain for the night Abdoulaye Doucoure headed in from close range after the Saints defenders failed to clear a corner to give the home side the ideal start.
But the visitors levelled soon after with their first real opportunity of the contest as centre-back Taylor Harwood-Bellis rose highest to plant home a thumping header from Charlie Taylor's pin-point cross.
Winger Jesper Lindstrom is still settling in with the Blues after joining on-loan from Napoli in the summer and displayed his rustiness by wasting several decent openings.
The Dane was twice thwarted when one-on-one with McCarthy, as well as being crowded out when finding himself in a good position inside the box.
The contest headed straight to spot kicks and it was the Saints who held their nerve to progress before celebrating in front of their jubilant supporters.
With ties also being played next week, Martin’s men will not find out their fourth round opponents until the draw takes place on Wednesday, 25 September.
Everton pay the penalty once more
A wretched season for Everton suffered another blow as they were knocked out of the competition for the fifth time in the last seven years on penalties.
And it had to be Young that was the villain of the piece as the mood threatened to turn mutinous at his introduction on the hour mark.
Looking for a winning goal, Dyche decided to replace striker Beto with full-back Young and it did not go down well with the home supporters, loudly jeering the move with audible obscenities thrown in the direction of the manager.
"That is the tough thing about football, it is a tough industry" Dyche said of the reaction. "The crowds have opinions about varying players and that is one of them things. He is certainly a tough customer mentally.
"I totally understand it, Young is old and wise enough to know this is the way the industry is. He is a fantastic professional but the fans have a right to say what they want to say and I am never going to question that.
"Inevitably we wanted to win the game and we haven't done. After piecing together a team this morning, with three players going down ill overnight, I think we have given as good as we can get.
"We have got 12 outfield players currently fit."
Dyche had stressed before the game that the league is the priority, but this was a missed opportunity to kickstart a faltering campaign which sees them lie bottom of the table after four games.
The triumph, though, will provide a huge boost to the confidence of Southampton, who were heavily beaten at home by Manchester United last time out and, like their opponents, have zero points so far.
They had a couple of chances to win it in the closing stages but Ben Brereton-Diaz struck straight at Joao Virginia after a bustling run, while lively substitute Tyler Dibling fired over following a mazy run.
Both teams have hugely important games on Saturday in a bid to pick up their first points, with Everton travelling to Leicester while Southampton host fellow promoted side Ipswich.
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