The Dragons (27-5) used an 11-2 run early in the second half to stretch a seven-point lead to 41-25. The Monarchs got within 46-38 with 7:58 to play, but Drexel answered with a 9-2 burst over the next 1 ½ minutes to reach its first CAA final since the 2002 season.
Drexel advanced to the CAA tourney final Monday night.
Kent Bazemore and Chris Cooper had 12 points each to lead the fourth-seeded Monarchs (20-13), who had won the last two tournaments.
Bazemore got his points on 6-for-20 shooting and wasn't alone as ODU shot just 33 percent and missed 15 of 18 3-point tries.
Chris Fouch hit four 3-pointers and added 16 points for the Dragons.