John Terry opened the scoring for the dominant hosts in the 31st minute when he turned home from close range after Diego Costa headed a corner goalwards.
Chelsea spurned a number of chances to extend their advantage, but Costa eventually made sure of the points on the hour mark when he fired a fine low shot past Adrian.
The Hammers, who started the day fourth in the table, failed to test Thiabut Courtouis at all and the 2-0 final scoreline didn???t reflect Chelsea???s complete dominance of the contest.
While the Hammers may well recover from this defeat to challenge for the top four this season, there is no doubt on this evidence that they some way off the level of Chelsea, who were in irresistible form all afternoon.
Jose Mourinho preferred Oscar over Jon Obi Mikel while the Hammers made three changes from their win over Leicester City, with James Collins, Mark Noble and Enner Valencia all starting.
It was Oscar who had the best early opening as Carl Jenkinson let Willian???s ball into the box bounce through for the Brazilian.
Fortunately for Jenkinson his mistake was not punished as Oscar fired over the bar from 10 yards out with just the keeper to beat.
Chelsea went close again in the 10th minute as Terry clipped a ball into the box for his fellow centre-back Gary Cahill, who rose well above Jenkinson but could only head over the bar.
The Blues were bossing possession and Cahill went close for a second time when he saw a fierce shot from inside the box blocked by Adrian.
Willian then tested the Hammers keeper with an effort from 25 yards before Hazard almost got in after some sumptuous one-touch passing.
Chelsea???s dominance eventually told on the half-hour mark when Costa headed a corner towards goal and Terry turned it in from a few yards out.
It was almost 2-0 minutes later as Adrian pulled off a fine fingertip save to turn Nemanja Matic???s shot around the post.
Costa then went close on a couple of occasions ??? seeing a deflected effort spin wide and shooting over from Branislav Ivanovic???s cross – as Chelsea continued to completely control the game.
The Hammers didn???t manage a shot on target in the first half and they soon found their goal under threat again after the interval as Hazard cut inside and drilled in a shot that Adrian had to palm away.
Sam Allardyce sent on Alex Song and Diafra Sakho shortly before the hour mark in a bid to spark his side into life, but Chelsea responded by putting the game to bed in the 62nd minute.
After a West Ham attack was broken up on the halfway line, Hazard moved the ball forward for Costa, who twisted and turned on the edge of the box before firing an excellent low shot across goal and into the corner.
Chelsea looked in the mood for more and came close as Costa volleyed over from Ivanovic???s superb back-post cross and then Adrian tipped Oscar???s free-kick over the bar.
The visitors almost snatched a late consolation when Morgan Amalfitano chipped a shot over the dive of Thibaut Courtouis, but saw the ball bounce back off the post.