After Saturday's first win of the season, away to Plymouth, Norwich looked favourites to win at home, especially when Rangers were reduced to ten men after just 25 minutes.
Instead, the visitors took the points with their only shot on target, when Martin Rowlands hit the back of the net with a sweetly struck free-kick eight minutes later.
From that point on the Canaries were out-muscled by a big, strong side.
Norwich kicked off attacking the River End goal, but made little progress against the well-organised QPR defence, although Matthew Connolly went into the book for a clumsy challenge on Antoine Sibierski after nine minutes.
Darel Russell did get a long-range shot on target after 15 minutes but Radek Cerny made a comfortable save.
Sibierski fired in a shot that looked destined for the back of the net but it was deflected for a corner.
Connolly was sent off after 25 minutes for a second bookable offence when he chopped down Matty Pattison.
A twice-taken free-kick saw the ten men take the lead when Rowlands' low, right-foot shot from 19 yards beat the defensive wall and David Marshall's despairing dive to his right.
The visitors continued to make light of the fact they were a man down and might quite easily have scored another goal before half-time.
At the interval Lee Croft replaced Arturo Lupoli, but his crosses from the right wing failed to trouble the Rangers defence.
John Kennedy limped off with an ankle injury and was replaced by Jonathan Grounds, on loan from Middlesbrough.
Shortly afterwards Wes Hoolahan made way for Jamie Cureton, who was soon forced to leave the field with blood pouring from a head wound. He returned swathed in a bandage.
Mark Fotheringham saw his free-kick turned round the post by Cerny and although Norwich finally put in some telling crosses, QPR weathered the storm to record their first away win of the season.