Sam Allardyce's men opened the scoring with an uncharacteristic goal from Andy Carroll. The gangly target man is known for his headed goals, but this time he outran the Leicester defence before dinking a deft chip over the onrushing Ben Hamer and into the net.
Midfielder Stewart Downing then made it two in the second half, bending a delightful shot past Foxes goalkeeper Hamer and into the corner of the net.
West Ham were largely in control for the entire game against a hapless Leicester City, but they mustered just two shots on target - which turned out to be the goals in a comfortable win.
West Ham stay fourth, just one point behind third place Manchester United and two points clear of fifth place Southampton. Whilst the Hammers have been remarkable this term, the situation is becoming bleak for Leicester.
Nigel Pearson's side sit rooted to the bottom of the table at Christmas, which is usually the Grim Reaper of stats for relegation threatened clubs, and they lie five points adrift of safety.