Michael Reddy and Peter Duffield both went wide with chances for the home side, before Darren Edmondson gave them the lead in the 33rd minute. Poor marking saw Edmondson free on the corner of the box, and Paul Musselwhite didn't move as he unleashed a shot into the top corner.
Musselwhite then saved with his legs from Duffield's header as the Minstermen had the better of the closing stages, but City held on for 1-0 at half time.
Peter Taylor made a double substitution at the break, bringing on Stuart Green and Lawrie Dudfield, and the change paid almost instant dividends.
After an early scare when Lee Nogan hit the crossbar, City got the equaliser in the 51st minute. Green found Dudfield on the right wing, and his cross went past Phil Jevons. However, Dean Keates was on hand to dig the ball out with his right boot at the back post, and level things at 1-1. The midfielder has now scored in both of the last two games, but later limped off with an ankle injury.
Green had an excellent chance to put City in front when he went one on one with Fettis. However, a poor first touch put him too close to the Northern Irishman, who blocked his run.
York then went down to ten men midway through the half when Chris Smith caught Ian Ashbee with a late tackle. Having previously gone in the book for upending Lawrie Dudfield, the referee showed him his second yellow card followed by a red.
But City couldn't make the extra man count, and were reduced to long range efforts and half chances, none of which beat Fettis so Peter Taylor and his side had to be content with a point.
City line-up (4-4-2): Musselwhite; Joseph, Whittle (Green 45), Anderson, Delaney; Regan, Ashbee, Keates (Holt 72), Melton; Alexander (Dudfield 45), Jevons.
Un-used subs: Deeney, Webb.