The midfielder, recently maligned for a lack of attacking end product, slotted home in the 87th minute with the visitors' only shot on target to down the resilient Rs
With Diego Costa and Loic Remy both out injured, Premier League leaders Chelsea were short of out-and-out attacking options at Loftus Road and looked set to end the match without troubling home goalkeeper Rob Green.
However, Fabregas - wearing a protective face mask after breaking his nose against Stoke City last weekend - drilled home a late winner to cruelly deny Chris Ramsey's side a valuable point in the fight against relegation.
|VIEW FROM LOFTUS ROAD
|By Liam Twomey
Nothing about this afternoon was pretty but Chelsea remain seven points clear at the top of the Premier League - and with one of their toughest remaining fixtures in the rear view. Cesc Fabregas's first goal since December could not have been better timed and it looks increasingly as if Jose Mourinho's men will secure a first title since 2010 in spite of declining energy levels and performances.
QPR played with real spirit here and might have changed the course of this afternoon had Matt Phillips found a way past Thibaut Courtois early in the second half, but this is a seventh consecutive home loss for a team whose results at Loftus Road have kept them from dropping into the Championship long ago. It is hard to see any other fate for this team than relegation now.
Chelsea are headed for considerably better things. John Terry, subjected to abuse all afternoon, led emphatic celebrations in front of the travelling Blues fans at the final whistle. They all know these three points bring the finish line ever closer.
But Fabregas, whose former club Arsenal are now Chelsea's main title rivals, had the final say, re-establishing a seven-point advantage at the top with his side's 100th goal in all competitions this season. QPR, meanwhile, remain two points adrift of safety.
A Remy muscle injury sustained in training on Saturday left 37-year-old Didier Drogba as Chelsea's only recognised striker, with Costa having already been ruled out for four matches with a hamstring problem.
And the veteran had justifiable claims for a back pass against Steven Caulker waved away early on.
The incident came after Willian had inadvertently found the right-hand post with a cross into the penalty area, but intentional goalscoring opportunities were at a premium for much of the opening period.
In fact, it took until the last two minutes of the half for either side to register a shot on target.
The ball fell to Charlie Austin just outside the penalty area, but Courtois got down well to his right to save the QPR forward's powerful strike.
Fabregas headed over from close range before the half was up to leave the game goalless at the break.
QPR almost snuck in front at the beginning of the second half when a Phillips cross, from a similar position to the delivery that saw Willian hit the woodwork in the first half, came close to beating Courtois at the far post, eventually bouncing wide.
And the Belgian stopper had to be on his guard again soon after, when Karl Henry – in for Niko Kranjcar as QPR's only change – teed up Clint Hill for a curling effort that was held by Courtois.
Phillips' shot from 12 yards out after 64 minutes perhaps represented QPR's best chance to snatch all three points and Fabregas pounced to punish that wasted opportunity.
A poor Green clearance invited pressure onto the home defence and, teed up by Eden Hazard on his 100th Premier League appearance, Fabregas sent a low strike into the bottom left-hand corner to seal the win.