Jose Mourinho’s side were well below their best in a scrappy west London derby, but the leaders stole a vital three points when Fabregas converted their only shot on target two minutes from full-time at Loftus Road.
The Blues are now seven points clear of second placed Arsenal and have a game in hand on the chasing pack, meaning four more wins from their remaining seven matches will see them crowned English champions for the first time since 2010.
While it was hardly a vintage performance in front of Roman Abramovich, who was watching from the stands as the Russian marked his 700th match as Chelsea owner, the gritty victory was invaluable as it gives Mourinho’s men greater margin for error heading into their showdowns with Manchester United and Arsenal over the next two weeks.
Defeat was cruel on third bottom QPR, who remain two points from safety despite matching their more illustrious opponents for long periods.
With leading scorer Diego Costa sidelined by a recurrence of the hamstring injury and Loic Remy hampered by a muscle problem sustained in training over the weekend, Mourinho had to deploy Didier Drogba as his lone striker.
Chelsea came close to taking a fortuitous lead in the seventh minute when Willian’s miscued cross from wide on the right dipped in front of QPR goalkeeper Robert Green and cannoned off the near post.
Man-of-the-match Joey Barton was a constant thorn in the side of the Chelsea players and worked tirelessly only to agonisingly end up on the losing side.
Fabregas, wearing a protective mask after breaking his nose against Stoke last weekend, was appropriately attired for such a physical encounter and his team-mate Thibaut Courtois was soon nursing a bruise as well when Charlie Austin left the Chelsea goalkeeper writhing on the turf after a full-blooded challenge.
Chelsea captain John Terry remains reviled at Loftus Road after he was banned by the Football Association in 2011 for racially abusing then QPR defender Anton Ferdinand, and inevitably he was subjected to a torrent of abuse from the home fans on just his second appearance at their ground since that ugly incident.
– Sound and fury –
Amid all the sound and fury, Chelsea were labouring to break down QPR’s well-drilled defence and even when Ramires got on the end of Drogba’s cross, the Brazilian midfielder found himself facing the wrong way and could only flick his volley wide.
Austin responded to an off-the-ball nudge from Terry by pushing the defender to the floor, much to the delight of QPR’s supporters.
And Austin went close to exacting even more satisfying retribution moments later when his stinging drive from 25 yards forced a fine save from Courtois.
Fabregas had a chance to end the stalemate on the stroke of half-time, but could only head Branislav Ivanovic’s cross tamely over from close-range.
Bobby Zamora was caught flat-footed by a Matt Phillips cross which begged to be tapped in by the statuesque QPR forward as it fizzed past him early in the second half.
When Clint Hill drew a save from Courtois moments later, Mourinho was quick to respond to Chelsea’s lethargy, sending on Oscar in place of Ramires.
Green had to be alert to tip over a scuffed clearance from Hill, but it was the hosts who threatened to break the deadlock when Phillips escaped Nemanja Matic’s attentions to fire in a close-range strike that Courtois brilliantly pushed away.
There was a surprising lack of energy and inspiration about Chelsea’s play, but to their credit they kept plugging away and stole the points in the 88th minute.
The catalyst was a poor clearance from Green which gifted possession to Chelsea and Eden Hazard took full advantage, playing a one-two with Oscar to open up the QPR defence before squeezing the ball back to Fabregas, who calmly slotted home his first goal since December.