Two own goals in the first half from defenders Antolin Alcaraz and Seamus Coleman gifted Southampton all three points as Everton missed the chance to climb above Arsenal into fourth spot.
Roberto Martinez's side were well below their best as they struggled to make any inroads against an energetic Southampton side and the result leaves Everton hoping for favours from other sides if they are to finish in the top four and claim a place in the Champions League next season.
Everton got off to the worst possible start when they gifted Southampton the lead inside the first minute through a calamitous gaffe from Alcaraz.
There looked very little danger on when Rickie Lambert floated in a cross from the left only for Alcaraz to inexplicably head it past Tim Howard for an own goal.
Everton tried to hit back and Romelu Lukaku wasted a decent opening on four minutes when Coleman picked him out inside the box, but the big Belgian striker blazed his shot over the top.
Southampton really should have doubled their lead on 21 minutes when Lambert got free down the left and picked out Steve Davis' perfectly-timed run into the box, but the midfielder slid his shot wide of the target with only Howard to beat.
Things got worse for Everton just past the half-hour mark and again they were their masters of their own downfall as Coleman put through his own net to double Southampton's lead.
Nathaniel Clyne burst down the right and fired over a cross which somehow Alcaraz and John Stones failed to clear and the ball bounced off the head of the unfortunate Coleman and into the bottom corner of the net.
Everton wasted a great chance to reduce the arrears on 38 minutes when Gerard Deulofeu worked space down the right and fired over a cross onto the head of Lukaku, who headed his attempt over the top from inside the six-yard box.
Southampton continued to look dangerous every time they went forward and they had claims for a penalty waved away before the break when Adam Lallana's cross appeared to strike the hand of Stones inside the box.
Southampton picked up where they left off at the start of the second half and Jack Cork should have done better when he volleyed wide from Luke Shaw's cross and Lallana had a sight of goal, but he blazed his shot well wide of the target.
Lambert was inches away from making 3-0 on the hour mark when his free-kick from 30 yards clipped the outside of the post.
Everton felt they should have had a penalty on 62 minutes when Leon Osman went down in the box under a challenge from Dejan Lovren, but to the amazement of the Everton midfielder referee Michael Oliver booked Osman for diving even though there appeared to be contact from Lovren on Osman.
Two minutes later Everton went close to scoring when substitute Aiden McGeady got to the byline and stood up a cross for Lukaku, who could only head his effort straight at Artur Boruc.
Everton had another claim for a penalty eight minutes from time when James McCarthy tangled with Lovren inside the box, but Oliver again turned down the visitors' appeals.
Howard denied Southampton a third goal in injury-time when he palmed away substitute James Ward-Prowse's fierce effort, but it did not matter as Southampton ran out comfortable winners.