The Canaries are dreaming of back-to-back promotions having lost just once in their last 14 games.
But Palace have not let in a goal at Selhurst Park in nearly 10 hours and rarely looked like conceding until City skipper Grant Holt came up with a dreadful late miss.
Wes Hoolahan had earlier forced a fine save from Julian Speroni, while the hosts went close through James Vaughan, Paddy McCarthy and Wilfried Zaha.
However, City's leading scorer Holt should have snatched the points as full-time approached only to blaze over the top.
With leaders QPR also being held, City will look on this as a missed opportunity to close the gap, which remains five points.
Norwich started confidently and Henri Lansbury, back on loan from Arsenal, nodded an early chance over before Andrew Crofts glanced a header wide.
Palace had a let-off when Alex Marrow's poor clearance fell to Hoolahan on the edge of the area and his curler was tipped over by Palace keeper Speroni, making his 200th appearance for the club.
Yet Palace almost stunned the Canaries on the counter-attack when Sean Scannell burst through and played the ball across goal for Everton loanee Vaughan, who was inches away from sliding it into an empty net.
They came even closer on the half-hour when Darren Ambrose floated a free-kick in from the left and Eagles skipper McCarthy's header flew just wide.
Vaughan, on his second Palace debut, was perhaps lucky to escape with only a yellow card when he caught Adam Drury with a stray arm.
City would certainly have felt aggrieved if the striker had found the top left corner of their goal with an 18-yard drive moments later, but he actually found the top left corner of the stand behind.
Early in the second half Vaughan rampaged down the left and sent in a low cross which Canaries keeper John Ruddy fumbled but Leon Barnett managed to clear with Neil Danns lurking.
Ruddy, who does a passable impression of City legend Bryan Gunn with his close cropped hair, did a far better job of keeping out a fierce drive from Scannell moments later.
The former Everton keeper came to his side's rescue agagin with a fine save to keep out substitute Zaha's angled shot.
And with five minutes remaining Selhurst held its breath as the ball bounced invitingly for Holt in the penalty area but the Norwich skipper crashed his shot high over the crossbar.