Wrexham remain top of the Blue Square Bet Premier despite drawing at York, but they are now equal on points with Fleetwood, who won 2-1 at fellow high-flyers Luton.
But Andy Morrell's side's better goal difference ensures they stay put.
York goalkeeper Michael Ingham kept the visitors at bay with some fine saves.
Jamie Tolley and player-boss Morrell's best first-half chances went begging and Lee Fowler was also frustrated after the break as Ingham shone.
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York City manager Gary Mills told BBC Radio York:
"Obviously we wanted to win today to close the little gap that's there but I thought it was a good game.
"Two good sides and both sides showed what it meant today.
"It's nice to get a clean sheet. There were chances either end and we've got to settle for a point.
"But it's a point that'll be important to us. They're top for a reason. We've given everything."