After Spurs and Manchester City both won their games at the weekend, Antonio Conte's side knew they had to win at the London Stadium to keep their significant lead over their league rivals in tact.
And win they did after Hazard overcame a minor training-ground knock from last week to hand Chelsea the lead in the 25th minute with his effort from a swift Blues counter-attack.
Diego Costa then made it 17 goals for the season with his 50th-minute strike from Cesc Fabregas' corner to leave him one short of 50 Premier League goals but secure all three points in the London derby clash, despite a late strike from Manuel Lanzini.
Chelsea now sit 10 points clear of Tottenham and 11 ahead of Pep Guardiola's City side, although they can cut the gap to eight should they win their game in hand against Stoke on Wednesday.
West Ham drop to 11th despite their optimistic showing against a side they beat in the same stadium in the League Cup back in October.
Indeed, Slaven Bilic would have been confident going into the derby game - despite being without the suspended Michail Antonio - after Andy Carroll was passed fully fit following his month-long absence with a groin injury.
The striker, who had scored in two of his last three games against Chelsea, proved the perfect target for an early cross from Sofiane Feghouli but found himself requiring medical attention soon after when Victor Moses' subsequent clearance caught the England international in the face.
After a few moments clearing up his bloody nose, Carroll returned to the pitch to continue to cause the Chelsea defence problems - with Robert Snodgrass often getting the better of Moses and Cesar Azpilicueta on the left flank to set up the Hammers forward with his crosses.
But despite the home side's bright start, Chelsea took advantage when Mark Noble's ball to Snodgrass saw the midfielder get dispossessed by N'Golo Kante, who then delivered it to Hazard in the 25th minute.
The Belgian raced clear to combine with Pedro before latching back onto the ball and running around the advancing Darren Randolph to score the opener in lethal fashion.
The goal helped settle Chelsea's nerves and, indeed, crush West Ham's early confidence but there were still opportunities for the Hammers in the first half - namely when Manuel Lanzini raced forward to combine with Noble but fired high.
The visitors reacted by going straight down the other end and attacking. Hazard played the ball in behind Costa who would certainly have scored but, instead, it fell to Moses whose follow-up effort was blocked by Aaron Cresswell.
Randolph then denied Pedro from close range to hand West Ham hope going into the break. But, after just five minutes of the re-start, any optimism the Hammers had evaporated when Costa doubled Chelsea's lead.
The goal - Costa's 49th in the Premier League - came from a Fabregas corner which was flicked into the path of the Chelsea striker by Pedro Obiang leaving Costa to knee the ball into the back of the net.
West Ham could have gotten one back but Moses - who spent last season on loan with the Hammers - showed off his superb defensive skills when the wing-back blocked Feghouli's effort before Jose Fonte headed over the bar.
Bilic's men continued to look positive going forward, but they were also forced to work hard in defence to contain Costa, who could have notched his 50th Premier League goal shortly afterward when he received Hazard's ball, swivelled and drove wide.
Lanzini, who had scored seven times in 11 Premier League London derbies before this game, then latched onto substitute Andre Ayew's ball from midfield to slot past Courtois but it proved only a consolation as Chelsea secured a victory over the Hammers by the same scoreline as they did back in August.
West Ham now drop from ninth to 11th while Chelsea continue to move a step closer to the Premier League title.