The England defender slotted home a loose ball on 16 minutes after the Saints failed to clear a corner and Seamus Coleman found his captain with a cut-back from the byline.
Southampton book-ended the game with impressive spells and went closest through James Ward-Prowse and Graziano Pelle in the first half.
But Everton held on to lift themselves to their highest league position since the turn of the year – 11th – and further away from relegation danger.
Southampton missed the chance to leapfrog Liverpool into fifth in the table, and they will feel hard done-by after arguably having the better of the game.
After assuming the early initiative, Pelle – on target against England during the international break – was denied a first league goal of 2015 when Tim Howard brilliantly clawed a looping shot away from the top corner.
But the hosts hit back and went close through Ross Barkley’s fierce shot past the far post, before Jagielka tapped Coleman’s low cross into the far corner for Everton’s opener.
Ward-Prowse, who was dangerous in a more advanced position than usual, threatened with a free-kick that shaved the outside of the side-netting, before testing Howard again minutes later.
Everton continued to benefit from the Saints’ lacklustre form in front of goal and Jagielka might have added a second before the interval when he rose above his marker but headed another corner over the bar.
But they could not create clear-cut chances in the second and were instead forced to show how they have improved defensively, keeping the Saints at bay – despite Ronald Koeman’s side finishing the game with four forwards – to earn a rare clean sheet.
Koeman threw on Dusan Tadic and Saido Mane after the hour mark and looked to play more directly into Pelle, but the Italian, who scored in the 1-1 friendly draw with England last Tuesday, was confined to just a single chance wide of the far post before the end.
Jose Fonte also fired at goal after a neat short corner found him just inside the area, but Jagielka and John Stones did enough to force his effort over the crossbar.
Southampton finished the game with three defenders after Koeman also threw on Filip Djuricic with 10 minutes left, but the Toffees stood firm to secure another vital win and move 12 points clear of trouble while the visitors missed the chance to climb above Liverpool and stay a point behind them in sixth.
Everton: Howard 8, Baines 7, Jagielka 8, Stones 7, Coleman 7, Barry 7, McCarthy 6, Osman 7, Barkley 7, Lennon 7, Kone 6
Subs used: Naismith 6, Besic 6
Southampton: Davis 6, Bertrand 6, Fonte 7, Alderweireld 6, Clyne 7, Schneiderlin 6, Wanyama 6, Ward-Prowse 7, Elia 6, Long 7, Pelle 6
Subs used: Mane 6, Tadic 6, Duricic 6
Man of the match: Phil Jagielka