Crawley, looking for back-to-back wins for the first time under Gregory, began the better team at the Broadfield Stadium and had a host of opportunities to break the deadlock, with the pick of the bunch falling to Gary Alexander.
Howeve the home side failed to clear a corner in the 22nd minute and Gleeson’s shot on the edge of the box left Paul Jones with no chance.
Karl Robinson’s side doubled their lead 14 minutes after the restart through Patrick Bamford, with the on-loan Chelsea striker latching on to Dale Jennings’ timely through-ball and notching his 16th goal of the season.
Substitute Sergio Torres, who replaced captain Dannie Bulman in the first half, was inches away from reducing the deficit, but his effort cannoned off David Martin’s crossbar.
Crawley’s misery was confirmed with six minutes left when Billy Clarke’s late challenge on Lee Hodson was deemed a red card.