Burnley will fancy their chances of reaching the next round after Rangers were unable to break down their resilient defence at Loftus Road.
And for all the home side's possession, it was Burnley who went closest to breaking the deadlock when Wade Elliott's stunning 26th-minute volley rattled the bar.
QPR rarely looked like finding the net and a shot from striker Samuel Di Carmine, which was comfortably saved by Clarets keeper Brian Jensen, was the most they could muster during a dismal first half.
They improved after the break and defender Kaspars Gorkss fired over the Burnley bar from 20 yards before Rangers appealed in vain for a penalty after Di Carmine went down under a challenge from Clarke Carlisle.
Emmanuel Ledesma, on loan at QPR from Genoa, replaced Lee Cook and sent a long-range drive wide.
Ledesma initially looked like causing Owen Coyle's side some problems but he quickly faded from the game and the 72nd-minute introduction of striker Patrick Agyemang also failed to bring Rangers to life.
The Clarets always looked dangerous on the counter-attack and Chris Eagles missed a good chance to put them ahead.
Steven Thompson got the better of Gorkss and threaded a great ball through to Eagles, who rounded keeper Radek Cerny but over-ran the ball and was unable to finish from a tight angle.
And with three minutes remaining, Burnley substitute Alan Mahon almost embarrassed Cerny with a speculative 25-yard effort that went just wide.