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The first effort of the game came from Adel Taarabt, who fired wide from 25 yards after two minutes.
The playmaker was involved once again on 11 minutes, dribbling past three Norwich defenders before dragging his shot just wide.
The Canaries had their first real chance of the game after 23 minutes when Robert Snodgrass put a powerful header wide of the post.
Chris Hughton's side began to look much more likely to get a goal and had another opportunity when Grant Holt headed towards goal, though a combination of Cesar and a defensive clearance kept the striker out.
Wright-Phillips had a chance on 35 minutes after Taarabt picked him out, though Javier Garrido pressured the winger into slicing his finish wide.
Taarabt almost gave his side the lead just before half time when his corner clipped the bar.
Norwich worked the ball well to create a chance for Hoolahan, but an impressive save from Cesar kept the playmaker's effort out.
The home side had a chance to take the lead on 55 minutes when the referee awarded them a penalty. Mackie raced onto Garrido's backpass, forcing Mark Bunn to bring the forward down in the area.
Taarabt stepped up to take the spot kick and saw his low drive palmed away by Bunn.
Taarabt tried to make amends for his miss on 61 minutes, firing a long-range shot at goal, but Bunn was equal to it once more.
Norwich came close minutes later when Bradley Johnson's stinging effort was saved well by Cesar.
Christopher Samba had a headed effort cleared by Holt after 67 minutes as QPR pushed for the winner.
Snodgrass came close again for Norwich on 78 minutes, but his curling effort was tipped wide by Cesar.