The defence froze in anticipation of an offside flag which failed to materialise allowing Craig Beattie to open the scoring just before the half-hour mark.
John Oster added a second with a delightful chip and although Matty Pattison pulled a goal back with half an hour left to play, the Canaries failed to conjure up an equaliser.
The visitors kicked off attacking the River End goal and took the game to Norwich in the early stages.
However, it took a splendid diving save from Julian Speroni to keep out Adam Drury's well-placed header when he got on the end of David Bell's free-kick.
The home side then enjoyed most of the possession without testing Speroni again.
In the 23rd minute David Marshall did well to force Beattie wide causing him to miss the target. But four minutes later he gave Palace the lead when the Norwich defence stood still and he was able to beat Marshall low to his right with a right-foot shot from eight yards.
It became 2-0 five minutes before the break when Sean Scannell laid the ball back to Oster and his delicate right-foot chip from 18 yards sailed over Marshall's despairing right hand and into the top corner of the net.
As the Canaries tried desperately to get back into the game, Speroni did well to dive on the ball as Leroy Lita attempted to round him.
The second half began with Speroni saving Lita's downward header from Drury's left-wing cross.
Norwich continued to push forward with much more purpose than in the first 45 minutes and pulled a goal back in the 61st minute, when Pattison got his head to Lee Croft's right-wing cross and beat Speroni's dive to his right from seven yards.
It was the 79th minute before City managed another shot on target, but this time Pattison's free-kick went straight to the keeper.
Palace then held firm to send the Canaries to their fourth home defeat of the season.