Saints hold their nerve as Everton pay price for lack of cutting edge
Everton 1 Southampton 1 (Southampton won 4-3 on pens)
Southampton put their difficult start in the Premier League to one side to beat Everton 4-3 on penalties and progress to the Carabao Cup fourth round.
Defender Cedric Soares scored the decisive spot-kick after misses from the hosts' £45m summer signing Richarlison and fellow substitute Theo Walcott, whose 85th-minute equaliser had sent the tie to a shoot-out.
Mark Hughes' side, who have won just once in the league so far this term, will travel to Leicester City in the next round.
It means Everton have now been eliminated in six of their last seven League Cup ties against top-flight opposition, despite Walcott cancelling out Danny Ings' first-half goal.
The hosts were nearly caught out in the third minute when Ings latched onto a simple long ball but goalkeeper Maarten Stekelenburg rushed from his line to save with his legs.
Later in the half, Everton's Ademola Lookman (20) tested Angus Gunn with a curling strike.
By then Everton were dominant but unable to make their possession count, and they paid the price just before half-time when Ings fired home.
But Walcott gave Everton a lifeline, collecting Oumar Niasse's pass to calmly equalise.
However once again Everton were made to regret their missed chances after Richarlison was first to miss in the shoot-out.
Stekelenburg denied Matt Targett but Walcott could not beat Gunn and Cedric duly set up a tie with the Foxes.