The Hammers had to come from a goal down to beat the resolute Foxes at the KingPower Stadium to record their 13th away win of the season.
A Jermaine Beckford header put Leicester ahead against the run of play after half an hour but Winston Reid pulled a goal back before half-time after a neat cross from Matty Taylor.
The second half continued like much of the first. The Hammers pilled on the pressure to ensure all three points and they were duly rewarded when Jack Collison struck the ball home from 25 yards.
The remainder of the game was dominated by the Hammers and they were unfortunate not to score another couple of goals to chip away at the goal difference between them and almost promoted Southampton.