Following Liverpool's 4-1 defeat at Arsenal earlier on Saturday, Ronald Koeman's Southampton had the chance to move up to fifth with a win at Goodison Park.
But although they made a promising start, the visitors fell behind against the run of play when Everton skipper Jagielka scored a scrappy opener - shortly after Tim Howard had pulled off a wonderful save to deny Graziano Pelle a first Premier League goal of 2015.
James Ward-Prowse almost restored parity with a curling free-kick but, despite their domination, Southampton could not force an equaliser before the break.
The second half continued in a similar fashion, with substitute Dusan Tadic Southampton's main threat, but Everton held on for their third top-flight win in a row as Koeman's side missed the chance to overtake Liverpool in the race for UEFA Europa League qualification.
But it was Southampton who started on top, Howard doing superbly to claw an effort from Pelle - whose last league goal came in the reverse fixture in December - off the line.
Southampton's usually rock-solid defence was a shambles, as they squandered several opportunities to clear from a corner, allowing Barry to square for Jagielka, who duly prodded home from close range.
The visitors came back strongly, with Ward-Prowse twice going close - first firing a free-kick just wide of the post before then forcing Howard into another fine save with a rasping long-range drive.
Koeman turned to Tadic and Sadio Mane for inspiration with half an hour remaining, and Tadic was involved immediately as he whipped in a superb corner towards the head of Shane Long, only for the striker to mistime his jump and direct a header wide.
Everton showed little attacking intent as the game drew to a close, but hung on to secure the spoils and move up to 11th, while Southampton's hopes of European qualification hang in the balance.
