Defeat meant Everton remained a point behind Arsenal, who currently occupy the fourth and final Champions League spot on offer to Premier League clubs, ahead of the Gunners’ match at home to Newcastle on Monday.
But Everton manager Roberto Martinez insisted the Merseysiders, whose final two league games of the season are against title contenders Manchester City and FA Cup finalists Hull, had not given up on a Champions League place.
“Not at all, from our point of view it doesn’t change at all,” Martinez told BT Sport. “We have had eight wins in 10 games, that’s a phenomenal return.
“Today was a real setback, but we’ll be ready for next Saturday,” the Spaniard added.
Everton, whose 2-0 victory over Manchester United last week led to their former manager David Moyes’s sacking by the English champions, were behind as early as the first minute courtesy of a bizarre own-goal.
Antolin Alacaraz got in front of the player he was marking to somehow head a cross from Southampton’s Rickie Lambert past goalkeeper Tim Howard.
And the visitors fell further behind shortly after the half-hour when Seamus Coleman diverted Nathaniel Clyne’s cross beyond Howard.
Victory saw Southampton remain eighth in the table.
Elsewhere, Fulham missed the chance to climb out of the relegation zone after Hull came from 2-0 down to secure a 2-2 draw at Craven Cottage.
Fulham’s Ashkan Dejagah curled a 55th minute shot into the top corner and three minutes later there was further joy for the home crowd in south-west London when Fernando Amorebieta headed in Kieran Richardson’s cross.
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Hull though pulled a goal back in the 75th minute when Nikica Jelavic nodded in from close range and the FA Cup finalists were level three minutes from time when Shane Long headed in Sone Aluko’s cross.
“It was very disappointing,” said Fulham manager Felix Magath. “If you are leading 2-0 at home, you have to see it through.”
West Bromwich Albion moved five points clear of relegation with a 1-0 win at home to West Ham.
Saido Berahino scored the only goal at The Hawthorns when he turned in Morgan Amalfitano’s centre in the 11th minute.
“Against Cardiff we drew, Tottenham we drew, then we drew with Liverpool, Chelsea and Everton so I really think we deserve that today,” said West Brom manager Pepe Mel.
“I think that we need to win one of our final three games to be safe.”
The Baggies victory helped them leapfrog Aston Villa after their Midlands rivals suffered a 4-1 loss away to Swansea that meant they were just four points above the bottom three.
Ivory Coast striker Wilfried Bony gave Welsh club Swansea a 10th minute lead before Gabriel Agbonlahor equalised for the visitors 12 minutes later.
However, Jonjo Shelvey restored Swansea’s lead with a goal-of-the-season contender in the 26th minute.
The midfielder controlled a clearance in the centre circle and volleyed a dipping shot over the head of back-pedalling Villa goalkeeper Brad Guzan.
Pablo Hernandez made it 3-1 in the 73rd minute before Bony completed the scoring with a late penalty — his 24th goal of the season.
Tottenham Hotspur moved to within three points of fifth-placed Everton, and a Europa League place, with a 1-0 win away to Stoke City secured through Danny Rose’s 33rd minute header at the Britannia Stadium.
Stoke were reduced to 10 men early in the second half when defender Ryan Shawcross was sent off after receiving a second yellow card for a studs-up challenge on Rose.
Saturday’s late Premier League fixture marks Ryan Giggs’s first match as interim player-manager of Manchester United when strugglers Norwich visit Old Trafford.
The race for the English title will intensify on Sunday when leaders Liverpool face second-placed Chelsea, five points behind, at Anfield.
Third-placed Manchester City, six points off the summit but with four league games remaining compared to the top two’s three apiece, are away to Crystal Palace.
At the other end of the table there is a relegation clash when bottom of the table Sunderland are at home to drop zone rivals Cardiff.
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