Richard Ross added 14 points for Old Dominion (3-20, 1-10), which had not won since upsetting Virginia 63-61 on Dec. 22 and had not beaten the Dragons since the 2009-10 season.
Corrigan, who had been the Monarchs' associate head coach, replaced Blaine Taylor, who was fired Tuesday. Taylor is the winningest coach in Old Dominion history.
There were five ties and 11 lead changes, with the Monarchs leading 30-26 at halftime.
Drexel (9-14, 5-6) took its final lead at 39-38, then Nick Wright's three-point play sparked an 11-0 Old Dominion spurt.
The Monarchs shot a blistering 65.2 percent (15 of 23) in the second half compared to 12 of 28 (42.9 percent) for the Dragons.
Drexel's Derrick Thomas had a season-high 18 points, while leading scorer Damion Lee (18.2 points) was held scoreless.