Tjaronn Chery’s brilliant left-footed strike – his third goal in his last five matches – put QPR ahead.
In-form keeper Alex Smithies played a big part in Rangers’ 24th-minute opener at Loftus Road, where the home side have grown in confidence since taking the lead.
Smithies threw the ball to James Perch near the halfway line and the full-back galloped down the left and delivered a perfect cross to Chery, who guided the ball into the net with a sublime volley.
Earlier, Sebastian Polter, back in the QPR starting line-up along with Clint Hill, Matt Phillips, Junior Hoilett and Alejandro Faurlin, went close with a long-range shot that went just wide.
And four minutes after his goal, Chery tried his luck with another left-footed effort that that flashed narrowly wide too.
Rangers went close again seven minutes before the break, when Phillips was just unable to connect with Hoilett’s left-wing cross.
QPR: Smithies, Onuoha, Angella, Hill, Perch, Faurlin Henry, Phillips, Chery, Hoilett, Polter.
Subs: Ingram, Konchesky, Tozser, Petrasso, El Khayati, Mackie, Washington.