The Reds' first away match of the season was settled by Mark Greaves' on 74 minutes after he headed home from a corner.
Brian Little's side went close when Carl Tremarco's effort was saved by substitute keeper Josh Mimms but Wrexham FC couldn't find a way through a resolute York defence.
The result will disappoint Reds' fans after their 5-0 opening day victory over Stevenage and Little will be looking for a big improvement when his side face Rushden on Sunday (August 17).
For a full match report and analysis, don't miss Friday's Evening Leader.
Ask Brian
If you have a question for Brian Little email it to digitalnews@nwn.co.uk and we'll ask as many as we can during our next video interview with the Reds boss this Thursday.
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