Rangers, who have had an equally inconsistent season, wrapped up the game in the first half thanks to goals from Marc Nygaard, Paul Furlong and Georges Santos.
The win relieves pressure on Rangers boss Ian Holloway as his side had not won in their previous five games, while Nigel Worthington will be wondering how a team that was in the Premiership last year has now conceded seven goals in two games.
After a quiet start the game exploded into life when Rangers went ahead after 10 minutes. The Hoops worked the ball across the midfield to Lee Cook who had plenty of time to put in a deep cross to the back post which Kevin Gallen expertly headed back across goal for the towering Nygaard to nod past Robert Green.
Questions will be asked in the Norwich defence over how Gallen and Nygaard were allowed free headers.
The Canaries had a chance to draw level minutes later. Darren Huckerby's run and turn gave him space inside the penalty area to pick out Ian Henderson running at the back post, but his shot deflected off Lloyd Dyer and trickled just past the post.
Henderson's miss became all the more glaring when Rangers doubled their advantage after 18 minutes.
Again Worthington will be looking at his defenders as Paul Furlong rose unchallenged to head Cook's free-kick past Green.
Rangers were now in control of the game but were forced into two changes after injuries to Nygaard and Marc Bircham.
Two minutes before half-time one of the subs, Santos, effectively put the game beyond doubt. Cook's corner was only half cleared by Dean Ashton and the much maligned Santos volleyed the ball past Green from the edge of the area with the help of a couple deflections.
Worthington threw on Rossi Jarvis and Dean Marney at half-time in a bid to salvage something from the game.
It was Marney who had Norwich's best chance in the second half when he blazed over an open goal after Ashton had brought a good save from Simon Royce.
Rangers also had opportunities to extend their lead through Dean Sturridge, Furlong and Tom Doherty but their first-half goals were enough.