Ronald Koeman's men missed the chance to leapfrog Liverpool in the Premier League table after slipping to a narrow defeat at Goodison Park
Ronald Koeman's side missed out on the chance to move into fifth following Liverpool's 4-1 defeat at Arsenal as, despite a promising start, they fell behind to Jagielka's scappy goal against the run of play.
James Ward-Prowse almost restored parity with a curling free kick but, despite dominating large part of the match Southampton could not force an equaliser before the break and Everton held on for the win.
The Toffees were without top scorer Romelu Lukaku due to a hamstring problem, and also revealed prior to kick off that Darron Gibson will be out for the foreseeable future with a fractured metatarsal.
However, Martinez was able to welcome back Gareth Barry from suspension, while Ross Barkley also came into the starting line-up after an impressive cameo for England in midweek against Italy.
That chance seemed to spark the hosts into life, James McCarthy going close before Jagielka nudged them ahead after 16 minutes.
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 sublime corner towards the head of Shane Long, only for the striker to mistime his jump and direct a header wide.
In response, Martinez introduced Muhamed Besic and Steven Naismith, with the latter having two penalty appeals waved away by referee Lee Mason within a minute of coming on.
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.