The home side kicked off attacking the Barclay End goal but fell behind in the seventh minute.
A fluent passing move by Fulham ended when the ball broke loose to Andy Cole.
He was left with only Robert Green to beat, and although the keeper got a touch, he could not prevent the ball finding the back of the net from the striker's low right-foot shot.
Norwich battled back but made little headway in midfield where they were out passed by the visitors.
In the 25th minute Mark Pembridge brought a good save from Green with a long-range shot.
Two minutes later Moritz Volz was booked for a late tackle on Thomas Helveg.
Phillip Mulryne's free-kick went straight to Edwin Van der Sar, as did a first time cross from Leon McKenzie.
As the half progressed Norwich seemed to be over anxious whereas Fulham were taking their time and finding their men much better.
Pembridge fired wide then Mathias Svensson tested the Fulham keeper with a low drive.
Darren Huckerby spoiled a good run from the halfway line when he let the ball run through to Van der Sar.
Papa Bouba Diop brought a save from Green with an incredibly fierce drive from long range.
Within seconds of kicking off the second period Fulham gave the ball away to McKenzie and conceded a corner when Carlos Bocanegra dispossessed Svensson with a well-timed tackle.
At the other end Cole whipped in a low cross from the right but Brian McBride arrived in the six-yard box too late to convert the chance.
Mulryne made way for Youssef Safri and Svensson was replaced by Mattias Jonson as Nigel Worthington tried to change the balance of play, but Fulham continued to defend in depth.
When Huckerby picked out Gary Doherty with a free-kick the former Spurs man headed wide.
Bocanegra was booked 10 minutes from time for a foul on Jonson and Cole was booked when he failed to retreat from a free kick.
Another Huckerby left-wing cross was headed wide of the far post by Jonson.
David Bentley fired over when he should have found the target and at the other end Green saved from McBride and then had to beat away fierce shots from Pembridge and Steed Malbranque.
In injury time Bentley again fired over as Norwich had to concede defeat in a game which had seen 50 fouls evenly distributed between the two sides.
MAN OF THE MATCH: Papa Bouba Diop (Fulham) Bossed the midfield and was a menace with his powerful long-range shooting.