The Middlesex batsman was well supported by Kent's Sam Northeast, who scored 89, and an unbeaten 57 from Peter Trego as the MCC salvaged hopes of an unlikely draw, reaching the close on 304 for four.
The MCC began the day on 73 for seven, chasing Warwickshire's 561 for six declared, and they were soon dismissed for a paltry 130 with Chris Wright claiming five for 35 and Oliver Hannon-Dalby three for 30.
Denly, who had suffered a migraine on day two, resumed his first innings before lunch and he top-scored with 47 before soon finding himself back at the crease again after the MCC were asked to follow-on.
The Warwickshire attack initially picked up where they left off, with MCC opener Jimmy Adams caught by Ian Westwood off spinner Paul Best for four, before Northeast and Denly built a second-wicket partnership of 156.
Warwickshire were affected by injuries, with Best and wicket-keeper Tim Ambrose off the field for the majority of the day.
Northeast had moved onto to 89 from 146 deliveries, including nine fours, when he was caught by Hannon-Dalby to give Wright his sixth wicket of the match.
Dale Benkenstein was then bowled for five by Rikki Clarke and Dawid Malan was caught for 28 before Trego went after the Warwickshire attack, blasting two sixes as he reached the close on 57 from 50 deliveries.
Denly brought up his century from 155 balls and he moved on to reach the close unbeaten on 119.
The MCC will resume on Wednesday trailing Warwickshire by 123 runs with six wickets in hand.