Antolin Alcaraz got the visitors off on the wrong foot after just one minute by heading the ball into his own net, and defender Seamus Coleman compounded the misery 30 minutes later with another header past shellshocked keeper Tim Howard.
Southampton remain in eighth place after the win with 52 points, five behind Manchester United, who play Saturday evening in their first match under manager Ryan Giggs.
Everton had been hoping to build on the momentum of last week's 2-0 win over the Red Devils, but remain a point adrift of Arsenal, who will host Newcastle United on Monday.
Southampton seems to have the number of the Liverpool side, who had won only one of their last 12 matches against the Saints entering Saturday's contest.
Everton's chances of a top-four finish and lucrative European football next season now look remote, as their final two matches of the season are against Manchester City and Hull City. Arsenal face strugglers West Brom and Norwich City after their Newcastle date.