Rovers led through Joel Lynch’s eighth minute goal, an advantage they doubled on the hour mark through Liam Feeney's close-range finish.
Their two goal advantage lasted for just a minute however, with Jake Bidwell reducing the deficit from the spot after Gordon Greer was penalised for a push.
However, they saw the game through to make it two wins from two at the start of 2017.
Owen Coyle made four changes for the FA Cup tie, with returns for David Raya, Ben Marshall, Elliott Bennett and Sam Gallagher.
However, with Craig Conway injured, and Marvin Emnes cup-tied, it was a near full-strength Rovers line-up for the game at Loftus Road.
Raya didn’t have to wait long for his first save, that coming in the fourth minute from a Grant Hall free-kick. The midifelder tried his luck from 25 yards after Jason Lowe fouled Ebere Eze, but it was easy for the Spaniard to collect on the bounce.
That came moments before Rovers threatened from a free-kick of their own, with Danny Graham flashing a header wide from an Elliott Bennett inswinger.
Bennett would then have a big hand in the goal which put Rovers 1-0 infront just eight minutes in. He won the ball deep in his own half and embarked on a terrific surging run forward. His cross was headed goalwards by Sam Gallagher, and although Matt Ingram saved, the ball hit Joel Lynch and rolled over the line.
It was reward for a bright start from the visitors, with Ben Marshall firing wide as the 10 minute mark passed.
That brought about something of a lull in the game, with QPR enjoying plenty of possession, but much of it in front of Rovers who were looking to play on the break.
And it was Rovers who would threaten next, as after a sustained spell of pressure, Charlie Mulgrew found room from Jason Lowe’s header, but his header was excellently blocked, before Sam Gallagher turned over, albeit from an offside position inside the six yard box.
Liam Feeney was looking particularly bright on the right wing, and forced several corners for his side.
Such was the frustration the hosts were feeling, Joel Lynch tried an effort from all of 35 yards after striding out from the back. Although well hit, it was wide of Raya’s post, as QPR waited for a standout chance.
A half which Rovers had looked comfortable in ended with a Ben Marshall strike going just over, as they took their advantage in to the break.
QPR started the second half stronger, looking for a way back in to the game. Elliott Bennett was forced in to an excellent defensive clearance just three minutes after the re-start, after Jamie Mackie had wriggled his way in to the box.