The Eagles came away pointless after getting off to the best possible start when Dougie Freedman set up Shaun Derry after just 74 seconds.
He gave Robert Green no chance with a clever right foot chip from 20 yards which curled inside the keeper's right hand post.
The Eagles then had to withstand prolonged spells of pressure from the Canaries.
Darren Huckerby brought the scores level from the penalty spot seven minutes before half time after he had been fouled by Curtis Fleming.
Malky Mackay secured three points for the Canaries when he touched in substitute Phil Mulryne's in-swinging cross from the left in the 89th minute.
Kevin Harper came close to equalising the Palace goal after seven minutes but the impressive Cedric Berthelin beat away his shot and the ball was cleared.
Gary Borrowdale was the first of five Palace players to be booked in the first half when he tripped Harper as the right winger beat him on the edge of the penalty area.
Huckerby beat the Palace keeper to a through ball but Berthelin recovered and managed to palm away the resulting shot.
On the half hour Hayden Mullins cleared the ball from underneath his own crossbar when Peter Crouch out-jumped Berthelin.
It was backs to the wall defending for Palace but the deadlock was only broken by the Huckerby penalty.
After being fouled Huckerby picked himself up and sent the keeper the wrong way with a low right foot shot to the keeper's left.
One minute into the second half Paul McVeigh put Huckerby through again but his snapshot was wide of the target.
Within two minutes he had an even better chance to double his tally but Berthelin was quickly down to turn the ball for a corner.
Borrowdale made way for Aki Rihalahti in the 50th minute.
On the hour Huckerby dribbled through the Palace defence but his shot was blocked and Damian Francis fired wide from the rebound.
In the 67th minute Harper appeared to be bundled over in the penalty area but referee Curson waved play on.
Two minutes later the Palace keeper reacted quickly to touch Huckerby's header onto the bar from McVeigh's corner.
Mulryne replaced Harper with 21 minutes left to play.
Iwan Roberts came on for Crouch six minutes from time and with the minutes ticking away the veteran striker saw the Palace keeper pull off another point blank save.
Unfortunately for Berthelin he was caught wrong-footed by Mackay at the death.