Two goals against the run of play proved enough for Sam Allardyce's men, leaving the visitors' hopes of beating the drop hanging in the balance despite a dominant performance
Matt Jarvis' goal from a cross and Kevin Nolan's fine finish proved the difference as the hosts held off a strong second-half performance from Wigan to earn the victory.
The result leaves the Latics in 18th, still three points from safety and with a real challenge to maintain their top-flight status.
Sam Allardyce named the same side that drew 2-2 with Manchester United in midweek, meaning the returning Mark Noble had to settle for a place on the bench. Wigan, meanwhile, brought back Gary Caldwell into a four-strong defence, while Callum McManaman came back into the side, with both Jean Beausejour and Franco Di Santo dropping out.
Allardyce's men were struggling to deal with Wigan's fluid attacks early on, but after Antolin Alcaraz had a tame first shot of the match the hosts eventually fashioned a chance of their own when James Collins' glanced header from a corner was met by Nolan, who could only divert the ball over.
It was nearly 1-0 at the other end immediately after when McManaman was put through one-on-one but Jussi Jaaskelainen stood firm to deny the Latics winger.
Joel Robles produced a strong palm to parry a swivelling Nolan's volley away, before the Hammers went in front, albeit against the run of play. The impressive Jarvis cut inside from the left and whipped in a dangerous cross which eluded three West Ham players and Joel before nestling in the far corner.
After Nolan had a penalty appeal waved away, Ricardo Vaz Te darted in front of Joel to meet Gary O'Neil's dangerous cross, but couldn't divert his header on target as the Hammers continued to impose their dominance towards the end of the first half.
But the Latics started brightly again after the break, and Arouna Kone nearly levelled things with a 25-yard volley which flashed just wide of Jaaskelainen's far post. At the other end, after Noble made a return from the bench, Andy Carroll hammered an effort wide before Robles was called into action, stopping a dangerous curling Diame strike.
Wigan were continuing to press and, after substitute James McArthur tested Jaaskelainen with a fierce long-range strike, Beausejour was denied by the Hammers goalkeeper as he tried to curl an effort into the top corner from the left-hand side of the area.
The West Ham shot-stopper was the hero again as he produced a stunning low stop to keep out McArthur’s driven effort from 12 yards out, and at the other end the hosts wrapped up victory with 10 minutes left as Nolan got on the end of Carroll's attempted bicycle kick to produce an excellent acrobatic finish of his own.
Carroll nearly got on the scoresheet himself as he broke past the Wigan defence, but with Joel rushing out, he snatched at the shot and it went well wide.
The Hammers held on though and move into the top half of the table, while Martinez's men have a real scrap to survive on their hands.