Trailing by seven in the first half, William & Mary (10-4, 2-1 Colonial) took the lead for good during a 27-2 run that included Omar Prewitt's go-ahead 3-pointer, and the Tribe made it 36-18 with 3:38 to go before the break.
Drexel (2-12, 0-3) twice closed the gap to single digits late in the second half, cutting the deficit to 70-61 with Tavon Allen's 3-pointer and then with Mohamed Bah's final bucket of the game.
Daniel Dixon added 19 points for William & Mary, which hit 53 percent of its 49 shots from the field and controlled the boards 29-22. Tarpey was 8 of 13 from the floor and 4 of 4 from the line.
Rodney Williams and Sammy Mojica had 13 points apiece for Drexel, which shot 54 percent from the field.