Neither team was able to carve open a clear-cut opportunity, with defences very much on top in a game which leaves Chris Hughton and Martin Jol looking anxiously over their shoulders at the basement battle unfolding beneath them.
Even the return of Dimitar Berbatov from a hamstring injury could not inspire Fulham.
Berbatov missed last weekend's defeat at Manchester United, and soon needed more treatment after he was caught in the face by a high boot from Norwich midfielder Bradley Johnson and had to go off to the changing room to have stitches in a bloodied nose.
Norwich almost made their man advantage count as Elliott Bennett's run down the left found defender Javier Garrido on the left side of the penalty area. The on-loan Lazio man pulled the ball back to Luciano Becchio, but his first-time shot lacked pace and was straight at Fulham keeper Mark Schwarzer.
Canaries defender Russell Martin, captain in place of the injured Grant Holt, planted a free header wide from Johnson's deep ball into the Fulham penalty area.
Emmanuel Frimpong, on loan at Fulham from Arsenal, was booked for tugging back Robert Snodgrass and referee Howard Webb had the yellow card out again when Bennett chopped down Hugo Rodallega as Fulham looked to break after they had cleared the free-kick.
Fulham started the second half brightly, with midfielder Steve 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 Snodgrass again the creator down the right before Bennett crashed in a goalbound effort which was blocked by Cottagers captain Brede Hangeland.
Johnson then stabbed wide from the edge of the box before Kei Kamara, on-loan from MLS side Sporting Kansas City, 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.