Josh Sargent and Jovon Makama were on target as Norwich boosted their survival hopes with a first away win under Philippe Clement.
Sargent converted Matej Jurasek’s cross in the opening minute of the second half to set the Canaries on course for a victory that lifts them to within a point of safety.
The visitors controlled the second period against a jaded Rangers side and might have increased their lead when substitute Makama was foiled by Paul Nardi.
But the young forward made it 2-0 in added time and, although Amadou Mbengue replied with a late consolation, it was not enough to deny Norwich their victory.
Both teams opted to shuffle the pack following their respective defeats three days earlier, with QPR boss Julien Stephan making eight changes to his starting line-up and Clement a mere three by comparison.
Those changes may have contributed to a disjointed first 45 minutes, with the game conducted at a lively pace without either side managing to get on top to any great degree.
Rangers went close through Steve Cook, whose glancing header from a corner flew across goal and Rumarn Burrell, latching onto a knockdown from strike partner Richard Kone only to be denied by Vladan Kovacevic at his near post.
The visitors’ best moment arrived shortly before the interval as Jacob Wright and Sargent combined to play Jurasek through, but his effort was neatly clawed away by Nardi.
However, the keeper could do nothing just seconds after the restart as Kenny McLean released Jurasek on the right and he motored past Rhys Norrington-Davies before whipping an inviting cross to the far post for Sargent to head in.
Norwich could have capitalised further as Pelle Mattsson’s volley whistled just over and Makama, who had just come off the bench, produced a shot on the turn that Nardi parried and Sargent could only bundle the rebound into the side netting.
Rangers pushed forward in the closing stages but offered little to threaten Kovacevic and Mathias Kvistgaarden broke to set up Makama, whose finish deflected in off Kieran Morgan for his fifth goal in as many games.
Kovacevic was finally beaten in the ninth minute of injury time, when Mbengue rifled past him from the edge of the box, but it made little difference as Norwich completed a league double over their hosts.
