Wolves' victory at home to Watford took them four points clear of Reading, who were forced to defend for much of the game but came close to taking all three points.
After back-to-back away wins, Rangers knew a victory against the Royals would take them into the play-off places and Heidar Helguson missed a golden chance to put them ahead after 11 minutes.
The Icelandic striker headed Damien Delaney's left-wing cross wide from inside the six-yard box and it proved to be QPR's best opportunity of the match.
Reading almost went ahead when Kalifa Cisse's shot was tipped away by Rangers goalkeeper Lee Camp, who also did well to keep out Leroy Lita's deflected effort early in the second half.
The home side had more possession but Reading always looked capable of nicking a goal and very nearly did so on 71 minutes when a goalmouth scramble ended with defender Matt Connolly blocking Kevin Doyle's attempt to bundle the ball over the line.
Rangers had another lucky escape after a mistake by Camp three minutes later.
Camp dropped Chris Armstrong's lofted free-kick but Stephen Hunt poked the loose ball wide of the target from 10 yards out.
With Helguson as a lone striker, Rangers struggled to create clear-cut chances and midfielder Hogan Ephraim coming on as a late substitute for the more defensive Gavin Mahon made little difference.