With top-four rivals Arsenal losing on Sunday, while Manchester United and Tottenham were not in action over the weekend, it gave Maurizio Sarri’s side a chance to boost their own Champions League qualification hopes and get one over on their London rivals West Ham, who had won two and lost two of their last four games.
And, following a slow start, Hazard lit up the contest midway through the first half with a fabulous solo strike, before Chelsea continued to dominate the opening period.
West Ham did show a little more endeavour after the break but Hazard wrapped up the win in the 90th minute with another superb finish as Chelsea move two points clear of fourth-placed Tottenham and three ahead of Arsenal, albeit having played a game more.
The Hammers remain down in 11th position on 42 points.
Chelsea boasted two changes from Wednesday's 3-0 Premier League win against Brighton as Antonio Rudiger came in for Andreas Christensen, while Gonzalo Higuain replaced Olivier Giroud.
There were five changes to the West Ham side after the 2-0 defeat by Everton last weekend as Pablo Zabaleta, Issa Diop, Robert Snodgrass, Pedro Obiang and Lucas Perez were replaced by Ryan Fredericks, Fabian Balbuena, Felipe Anderson, Chicharito and Mark Noble.
Chelsea started brightly but lacked any real punch in the final third, while the Hammers were growing into the contest when Hazard rocked them with a stunning individual goal on 24 minutes.
The Belgium international picked up possession midway inside the West Ham half and proceeded to breeze past Noble, before gliding between three defenders on the edge of the area and then placed a right-foot shot into the bottom corner beyond the dive of Lukasz Fabianski.
The goal gave the hosts a lift and they went close to a second on 27 minutes when Hazard picked the run of Higuain with a pin-point pass and the Argentinian slammed an angled drive off the outside of the post.
Chelsea should have had a penalty on 29 minutes when Hazard was going down the left side of the Hammers’ area before Marko Arnautovic blatantly barged him to the ground without getting near the ball.
On 35 minutes Hazard was again involved as he eased past Arnautovic before chipping a cross to the back post for Callum Hudson-Odoi to get a shot off at goal, only for Aaron Cresswell to get in a timely block.
Fredericks was on hand to prevent Chelsea going into the break with a two-goal lead on 43 minutes when he somehow managed to deflect Higuain’s on target effort from 10 yards wide of his own goal.
Chelsea started the second half where they left off in the first with Ruben Loftus-Cheek the creator on 48 minutes as he bustled his way through the middle before playing in Hazard and his reverse shot across the face of goal rolled inches wide of the far post.
West Ham had their first real opportunity on 54 minutes when Arnautovic picked up an Anderson ball inside the area and held it up before teeing up Manuel Lanzini whose effort from 15 yards was pushed away by Kepa Arizzabalaga.
The Hammers created another opening on 63 minutes when Cresswell tried his luck from around 25 yards and his effort swerved just wide of Kepa’s goal.
Chelsea seemed to weather the wave of pressure from the visitors and stepped up another gear.
And, they almost settled matters in the 79th minute when both substitutes, Giroud and Ross Barkley, failed to put the finishing touch to Hudson-Odoi’s low ball across the face of goal from the right.
Barkley then combined with Giroud in the 86th minute but, with the angle narrowing, the French forward’s effort was saved by the legs of Fabianski.
A stretching Giroud was again inches away from a killer second goal on 89 minutes when he just failed to get a touch on Pedro’s teasing ball across the six-yard area.
It was game-over in the 90th minute when Barkley picked out Hazard on the right side of the West Ham area and he took a touch before drilling a low right-foot effort past Fabianski and into the far corner.