Southampton missed the chance to leapfrog Liverpool in the Premier League as Phil Jagielka gave Everton a 1-0 win on Saturday.
Phil Jagielka's early goal was enough to secure Everton's third consecutive Premier League victory as it won 1-0 over Southampton.
Following Liverpool's 4-1 defeat at Arsenal earlier 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 its domination, Southampton could not force an equalizer before the break.
The second half continued in a similar fashion, with substitute Dusan Tadic Southampton's main threat, but Everton held on for its 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.
Already shorn of injured top scorer Romelu Lukaku, Everton was dealt another blow prior to kickoff when it was revealed 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 lineup.
But it was Southampton that started well, with Howard doing superbly to claw an effort from Pelle — whose last league goal came in the reverse fixture in December — off the line.
That chance seemed to spark the hosts into life, with James McCarthy coming close before Jagielka nudged them ahead after 16 minutes.
Southampton's usually rock-solid defense was a shambles, as it 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 coming 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 toward 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.