Mick Harford, taking charge of his first home match as caretaker manager, made three changes to the QPR side that lost 4-2 at Colchester last week, while Peter Grant kept faith with nine of the 11 that drew 0-0 against Scunthorpe six days ago.
And both sides started by showing a lack of confidence that demonstrated why they are in the relegation zone, with Mikele Leigertwood shooting tamely wide for the home side only seven minutes in.
QPR's Hogan Ephraim, on loan from West Ham, looked most likely to make the breakthrough, smacking in a shot on the half-hour that Norwich keeper David Marshall did well to stop.
And it was mostly one-way traffic for the first 45 minutes as Norwich looked like a team that hasn't scored for five games.
They weren't helped by boss Grant's decision to play Darren Huckerby up front on his own as the former Coventry man was caught offside more often than not.
Rangers nearly took the lead a minute into the second half when Martin Rowlands' long-range effort smacked off Marshall's right-hand post with the keeper nowhere near it.
Rowan Vine was then denied what seemed a certain penalty when he was thrown to the ground by Jason Shackell, with Harford's side dominating the start of the second period.
And with 25 minutes to go the home side deservedly took the lead when Rowlands smashed home a penalty after Vine had been fouled by Ian Murray in the box.
Gareth Ainsworth nearly doubled the lead moments later with a 25-year volley before, from the resulting corner, Damion Stewart forced Marshall to tip over his header.
Marshall then saved acrobatically from Rowlands as QPR looked rampant, and the Scottish goalkeeper excelled himself again when denying Ephraim.
Rangers ran the clock down comfortably and there were jeers from the Norwich end at the final whistle as their side looked more like relegation possibilities than promotion-chasers.