Rovers had the better of the first-half chances, Andy Cook and Lois Maynard going close early on before Jeff Hughes had a close-range effort well saved by Kyle Letheren in the closing stages.
The game swung in York's favour after Hughes was sent off for a challenge on Richard Brodie in the opening minutes of the second half but Tranmere threatened again when James Norwood headed the ball against the crossbar.
Justin Johnson fired well over for York in injury time as they failed to make their numerical advantage count.
Match report supplied by the Press Association.
Match ends, York City 0, Tranmere Rovers 0.
Second Half ends, York City 0, Tranmere Rovers 0.
Lee Vaughan (Tranmere Rovers) is shown the yellow card.
Substitution, York City. Scott Fenwick replaces Daniel Nti.
James Norwood (Tranmere Rovers) is shown the yellow card.
Substitution, York City. Justin Johnson replaces Jake Wright.
Jeff Hughes (Tranmere Rovers) is shown the red card.
Second Half begins York City 0, Tranmere Rovers 0.
First Half ends, York City 0, Tranmere Rovers 0.
Andy Cook (Tranmere Rovers) is shown the yellow card for a bad foul.
Shaun Rooney (York City) is shown the yellow card.
Liam Ridehalgh (Tranmere Rovers) is shown the yellow card.
First Half begins.
Lineups are announced and players are warming up.
Ten-man Tranmere halted their two-game losing run in the National League with a goalless draw at York.