It took the Blues 88 minutes to break the deadlock at Loftus Road after a dogged performance from Chris Ramsey's men.
Eden Hazard and Oscar worked a lovely one-two down the left flank before the Belgian squared it to Cesc Fabregas, whose low drive from 16-yards fired past goalkeper Rob Green.
Jose Mourinho's side had failed to register a single shot on target before Fabregas' strike and it was Rangers who enjoyed the better of a disappointing game, with Matt Phillips squandering an excellent chance in the second half.
Fabregas, however, broke the home side's heart with his fifth goal of the season to keep Chelsea's title charge firmly on track, while QPR remain 18th and two points adrift of safety.