Danny Sumner scored 14 points for William & Mary (10-8, 6-2 Colonial Athletic), which hit 14 3-pointers, including two in overtime.
The teams were evenly matched throughout, finishing the first half tied at 33 and regulation deadlocked at 65-all after Rodgers hit a jumper with 20 seconds left.
In the overtime, William & Mary raced to a five-point lead before Drexel rallied. Rodgers hit a pair of free throws to pull the Dragons within 71-68, and Tramayne Hawthorne hit a pair of free throws to make it 71-70.
Sumner dropped in a layup to put William & Mary ahead by three with 1:14 remaining, before Rodgers scored to cut Drexel's deficit to 73-72. But Hawthorne's 3-point try with four seconds left missed the mark.