The Chairboys finally broke through 12 minutes from time when McGleish slotted home from close range after a Mike Williamson assist.
Wycombe had the first decent chance after 18 minutes when Delroy Facey set up Russell Martin, but he blazed over.
Martin beat John Danby in the Chester goal a minute later with a 30-yard shot but it fell narrowly wide.
After the break, John Murphy put strike partner Paul McManus but he shot over.
On the hour-mark, the home side almost took the lead when the dangerous looking Facey burst into the City box but his shot smashed against the post. With 20 minutes left a Martin corner found Stefan Oakes and he too struck the post before McGleish pounced.