Gary Hooper struck with 30 minutes gone after a flowing Norwich move.
Despite plenty of effort, Palace were lacklustre with the ball in the first half.
In the second, Pulis's men were the better side, but were unable to find the back of the net.
Sports Mole takes a closer look at the action between the teams at Carrow Road.
On target 3
On target 3
Was the result fair?
On the balance of play, just. But make no mistake, Palace were the better team in the second half. What let them down was their final pass and they failed to create enough. Norwich were good in the first half, steady in the second.
The first half showed that on their day, Norwich are good with the ball and pose a threat when going forward. Nathan Redmond was a constant menace down the wings, but his performance faded as the game progressed. What Chris Hughton will be pleased with is that despite a wobble in the second half, his players were resolute. This was their third home win of the season. Now they need to improve away from Carrow Road.
Crystal Palace's performance:
Despite the result, Pulis will be pleased with how his players responded after the interval. However, when chances did fall their way, Palace were wasteful. Pulis will want to see more quality in the final third, but the signs today were positive.
Sports Mole's man of the match:
Nathan Redmond: His performance may have faded, but Redmond was a source of excitement whenever he received the ball and he played a part in the goal. Norwich look more threatening with him in the team.
With the clock ticking towards 90 minutes, Cameron Jerome had a good chance to level the scores, but rushed his shot and got it all wrong.
Norwich: The Canaries travel to Merseyside to play Liverpool on Wednesday night.
Crystal Palace: The Eagles welcome West Ham United to Selhurst Park on Tuesday.