A first half cross from Matt Jarvis and an acrobatic second half goal from Kevin Nolan proved too much for Latics at Upton Park.
Latics controlled possession in large spells but were limited in their chances as the home side defended deep and tightly.
Roberto Martinez made two changes from the 1-0 defeat to Manchester City on Wednesday as Callum McManaman came back in for Franco Di Santo and Jean Beausejour dropped to the bench as Gary Caldwell returned to start.
In the opening ten minutes West Ham sat back and soaked up Latics' passing rhythm, making it difficult for chances to be created.
The hosts progressed to look dangerous from set pieces and aerially from crosses but, on 21 minutes it was the cross that proved crucial rather than what was on the end of it.
Jarvis found space on the left wing and cut back onto his right foot for the cross, as the ball came in Mohamed Diame reached to flick it on with his toe but, it avoided everyone and bobbled into the bottom corner of Joel Robles' goal.
The goal was arguably against the run of play and the first half ended how it started, with Latics searching for a golden opportunity.
Latics made their second substitution of the game at half time, when McManaman was replaced by James McArthur, after Antolin Alcaraz made way for Jean Beausejour just 16 minutes in.
As the second half progressed, Latics built up more momentum and poked and prodded the West Ham defence as they tried to equalise.
On 72 minutes that crucial chance looked like it had arrived when Shaun Maloney crossed low from the right after spinning around the defender but, Jussi Jaaskelainen made an excellent save from McArthur's close range connection.
Despite possessional dominance in the second half, Latics couldn't find a way past Jaaskelainen and with 10 minutes remaining, Nolan sealed the points for West Ham as he acrobatically helped in a high over head kick from Andy Carroll from close range.