Kale Abrahamson's 4-point play midway through the second half started Drake's 11-0 run for a 65-49 lead. Bradley battled back to get within six points with 1:04 left, but Reed Timmer answered with two free throws as Drake closed by making 6 of 8 from the stripe.
Timmer finished with 19 points for Drake (6-16, 1-9), which ended a nine-game losing streak. Abrahamson had 13 points.
Drake has won nine of the last 12 meetings since the 2011-12 season.
Antoine Pittman scored 17 points for Bradley (3-20, 1-9), which has lost five in a row and 11 of 12. Luuk van Bree added 13 points, Dwayne Lautier-Ogunleye had 12 and Donte Thomas 11.