Brazilian playmaker Oscar broke the deadlock during the first half, before QPR striker Charlie Austin equalised after the restart.
However, Hazard sealed all three points for the home team when he scored from the penalty spot with 15 minutes left to play.
Here, Sports Mole has rated the performances of each of the players on show at Stamford Bridge.
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Thibaut Courtois: QPR scored with their one shot on target, which will no doubt have annoyed Courtois. Aside from that, he had very little to do. (6/10)
Branislav Ivanovic: With his bright yellow boots, Ivanovic raided up and down the right flank all afternoon. While his style might not be overly easy on the eye, it is very effective. (7/10)
John Terry: One poor clearance almost resulted in a goal for Sandro, but apart from that, it was a solid outing from the Chelsea skipper. (6/10)
Gary Cahill: Similar to Terry alongside him, Cahill carried out his duties with minimal fuss. He made one sliding challenge late on to deny Austin a clear run on goal. (6/10)
Filipe Luis: Continuing in the team during the absence of Cesar Azpilicueta, Luis did well. He supported the attackers whenever he could and even had a shot at goal, which flew over. (6/10)
Cesc Fabregas: Yet another assist for the Spaniard - his ninth of the season. In setting up Oscar for the opener, Fabregas showed quick feet to get away from the QPR defence. (7/10)
Nemanja Matic: His presence in the middle of the pitch allowed the likes of Fabregas to get forward. However, he was uncharacteristically wasteful in possession on occasions. (5/10)
Oscar: The Brazilian is starting to score goals - impressive ones as well! His finish with the outside of his right boot was stunning and it rounded off a lively performance. (7/10)
Willian: A quiet outing from the Brazilian and it came as little surprise when he was replaced in favour of Didier Drogba. (5/10)
Eden Hazard: He flitted in and out of the game, but was around for the crucial moment when he was brought down inside the area. The Belgian then rolled the ball in from 12 yards with ease. (6/10)
Diego Costa: Having just returned from injury, the Spaniard looked a little rusty. To his credit, though, he did hold the ball up well and brought others into play. (6/10)
Didier Drogba: The club legend was unable to continue his recent form in front of goal. (5/10)
Andre Schurrle: The German gave a reminder to his manager of how dangerous he can be when he called Robert Green into action with a good low effort. (6/10)
Ramires: Brought on with a few seconds left to play to waste some time, so it would be unfair to give him a rating.
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Robert Green: A great performance from the former England international, who made crucial stops in both halves to keep his team in the game. (8/10)
Mauricio Isla: The Chilean, perhaps under instruction, did not get forward too often, but he did make some good challenges and interceptions. (6/10)
Richard Dunne: He may not be the quickest defender, but Dunne reads the game extremely well. Few defenders have kept Costa quiet, but Dunne managed it. (7/10)
Steven Caulker: Some of the credit for keeping Costa at bay should also go to Caulker, who used his pace well on occasions. He looks much more settled alongside Dunne, rather than Rio Ferdinand. (7/10)
Yun Suk-Young: The left-back is becoming a regular in the starting lineup and he showed why with another good performance. Defensively he was sound and there was the odd occasion when he joined in attacks. (6/10)
Sandro: Harry Redknapp has bemoaned Sandro's recent injury problems and the Brazilian showed just how good he can be. It was an impressive all-round midfielder's performance, full of tenacity and determination. (7/10)
Karl Henry: He seemed to struggle at times with the pace of the game, but that did not stop Henry from making some important tackles. (6/10)
Leroy Fer: For such a physical presence, you cannot help but want a bit more from Fer. The Dutch international was quiet today and made little impact on proceedings before he was replaced. (5/10)
Junior Hoilett: It seemed a little harsh to bring the winger off because he had started the second half so brightly, despite his final ball sometimes leaving a lot to be desired. (6/10)
Eduardo Vargas: The Chilean was lively up and down the right flank, but his error in giving away the penalty cost his team dearly. (5/10)
Charlie Austin: Earlier in the season there were question marks over Austin and his ability to score goals in the Premier League. Those doubters will have been silenced again today with another goal in a good outing from the striker. (6/10)
Bobby Zamora: The tall centre-forward has caused problems to defences in recent weeks, but he was kept largely quiet by the home rearguard. (5/10)
Armand Traore: Brought on with only a few minutes left to play, during which he rarely got a touch of the ball. (5/10)