While a point will edge both sides closer towards safely, there was little creative spark. New Norwich signing Luciano Becchio, in for injured captain Grant Holt who suffered a back spasm on Saturday morning, headed a couple of half-chances wide.
Even the return for Dimitar Berbatov from a hamstring injury could not inspire Fulham, with a 25-yard effort from Steve Sidwell at the start of the second half about the best of the visitors' few chances.
Berbatov missed last weekend's defeat at Manchester United, and soon needed more treatment after he was caught in the face by high boot from Norwich midfielder Bradley Johnson and had to go off to the changing room to have stitches in a blooded nose.
Norwich almost made their man advantage count as Elliott Bennett's run down the left found defender Javier Garrido in the left side of the penalty area. The on-loan Lazio man pulled the ball back to Becchio, but his first-time shot lacked pace and was straight at Fulham keeper Mark Schwarzer.
At the other end, Damien Duff saw his effort blocked by Michael Turner, while Berbatov's clever flick released Duff on the overlap, but his angled shot was deflected over the crossbar. Norwich defender Russell Martin, captain in place of Holt, planted a free header wide from Johnson's deep ball into the Fulham penalty area.
Fulham started the second half brightly, with midfielder Sidwell testing Norwich keeper Mark Bunn with a 20-yard effort. Norwich defender Sebastien Bassong then took the full force of Bryan Ruiz's strike in his face as the visitors stepped up a gear.
The hosts finally produced some pressure of their own as the hour mark passed, with Robert Snodgrass again the creator down the right before Bennett crashed in a goalbound effort which was blocked by Cottagers captain Brede Hangeland.
Fulham made a change after 64 minutes when Emmanuel Frimpong was replaced by Holland defender Urby Emanuelson. Both sides made a substitution with 15 minutes left as Mladen Petric replaced Hugo Rodallega for Fulham, while Norwich sent on Canada forward Simeon Jackson, as Bennett was withdrawn.
Johnson stabbed wide from the edge of the box before Kei Kamara came on to replace Becchio for the closing stages of a match which desperately needed a spark. However, the Sierra Leone international's main contribution was to clatter into Schwarzer at a corner, as the game fizzled out.