Harry Redknapp's side dropped points at home for only the second time this season and are now behind new leaders Burnley on goal difference.
This term Rangers have developed a happy knack of grinding out 1-0 victories from similarly uninspiring matches, but their goal touch for once deserted them.
Their best chance fell to Charlie Austin, who was denied by a combination of the woodwork and Rovers keeper Simon Eastwood in the second half.
But Rovers also had their opportunites, particularly in the first period, and will feel they could have left Loftus Road with only their second away win of the campaign.
Eastwood was handed his league debut after Rovers boss Gary Bowyer axed Jake Kean following some recent costly errors, but Rangers barely tested the new man in a ragged first half.
Instead Rovers should have gone in ahead at the break after creating a string of chances, the clearest of which fell to Jason Lowe.
Ben Marshall's cross from the left fell to Lowe at the far post but his half-volley was headed off the line by Clint Hill.
Chris Taylor should have hit the target when he met a cross from Tommy Spurr but his header flew over, and moments before half-time Jordan Rhodes nodded wide.
For Rangers Benoit Assou-Ekotto blazed over, Eastwood comfortably held a curling Joey Barton free-kick and Matt Phillips' shot was deflected wide by Scott Dann.
But the hosts were brighter after in the interval and came close to breaking the deadlock from a swift counter-attack after 55 minutes.
Rhodes should have got a shot away in the Rangers penalty area but could not get the ball out from under his feet and was robbed by Barton.
The midfielder fed Andrew Johnson, whose low cross found Phillips but he placed his shot too close to Eastwood.
Austin's big chance arrived in the 70th minute after a fine run down the left by Assou-Ekotto.
His low cross was met by the 10-goal striker six yards out but his effort came off the inside of the post, hit the bemused Eastwood and bounced back out.
Gary O'Neil drove back across goal but Austin's feet were in a tangle so the ball rolled harmlessly wide, and with it went Rangers' chances of victory.