Captain Mark Greaves grabbed the only goal as York continued their winning start to the season.
The defender beat three Wrexham players at the far post to head home a 74th-minute corner.
Simon Rusk forced a good save out of Dragons keeper Gavin Ward soon after and Ben Wilkinson was earlier denied.
Wrexham's best effort came on 70 minutes when Carl Tremarco's 30-yard drive was brilliantly saved by substitute keeper Josh Mimms.
Mimms came on after York keeper Artur Krysiak was forced off with what appeared to be a rib injury just before the break.
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Subs Not Used: Kelly, Shepherd.
Booked: McBreen, McGurk.
Goals: Greaves 74.
Wrexham: Ward, Spender, Nathaniel Brown (Steve Evans 70), Kempson, Tremarco, Simon Brown (Baynes 81), Kearney, Smith, Aiston, Louis (Marc Williams 80), Whalley. Subs Not Used: Anthony Williams, Taylor.
Booked: Tremarco.
Att: 2,603
Ref: J Waugh (Sheffield).
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