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 cut the gap, which remains at five points.