Unchanged York dominated the first half, forcing eight corners, but the closest they came was when a cross from Danny Learns skimmed the bar.
Michael Ingham made the one notable save our the half when Wimbledon’s Jack Midson burst through the middle just before the break.
Jamie Reed came off the bench and hit into an empty net after being fed by Jason Walker inthe 63rd minute.
The visitors equalised when sub Charlie Strutton saw his free-kick deflect in off a post.
Seb Brown then made a flying save to deny Walker a late winner.