Andy Cole's early strike gave Fulham plenty to smile about as the Cottagers edged further away from the relegation zone at Carrow Road.
Cole took just seven minutes to drill the ball under the keeper after a great back flick from Brian McBride.
Mark Pembridge almost added two more before the break but Norwich improved their attacking in the second half.
Darren Huckerby, Leon McKenzie and substitute Matthias Jonson had shots but Fulham held on for a vital win.
Fulham may have grabbed their league win in four matches but it left Norwich firmly entrenched in the bottom three.
Cole's sixth goal of the season in the Premiership was the first real chance on target for either side in a frantically-charged encounter at Carrow Road.
Both teams struggled to hold onto the ball before McBride, making his first Premiership start in six weeks, capitalised on a Fulham break to send Cole through.
Norwich's Darren Huckerby and Leon McKenzie desperately searched for a quick reply, teasing the away side's penalty area but never finding the final touch.
Pembridge came close to extending the Cottagers' lead twice in the first half.
He was denied from the edge of the box by the quick reactions of Canaries goalkeeper Robert Green in the 25th minute and shot wide just before half-time.
A minute later, Matthias Svensson tested Fulham keeper Edwin Van der Sar for the first time when he drilled a shot into the bottome left-hand corner.
After the break, Norwich looked slightly improved with Huckerby and McKenzie doing most of the pushing but still failing to trouble the visitors.
With 15 minutes to go, Canaries boss Nigel Worthington spiced up the attack by bringing on Jonson for Svensson.
It seemed to do the trick as the Cottagers were forced to withstand a barrage of shots from Huckerby, Jonson and Gary Doherty.
But, after McBride squandered a late chance to add a safety cushion, Fulham held on for a much-needed victory away from home.
Norwich: Green, Edworthy, Fleming, Doherty, Drury, Bentley,
Helveg, Mulryne (Safri 62), Huckerby, McKenzie,
Svensson (Jonson 68). Subs not used: McVeigh, Ward, Shackell.
Fulham: Van der Sar, Volz, Pearce, Rehman, Bocanegra,
Legwinski, Diop, Malbranque, Pembridge, McBride, Cole. Subs not used: Knight, Flitney, Radzinski, Hammond, Rosenior.
Booked: Volz, Bocanegra, Cole.
Goals: Cole 7.
Ref: A Wiley (Staffordshire).