Seth VanDeest made two free throws with 1.2 seconds left to force overtime, and Drake dominated the extra session to beat Bradley 92-84 on Wednesday night and snap a four-game losing streak.
Bradley looked to have the game in hand after Will Egolf's 3-pointer with 28 seconds to play put the Braves up 70-65.
But the Bulldogs got a three-point play from Richard Carter before Bradley's Tyshon Pickett was fouled and missed the front end of a one-and-one.
VanDeest then rebounded a missed 3-pointer, was fouled and made both shots.
Jordan Clarke led the Bulldogs (12-15, 6-10 Missouri Valley) with a career-high 20 points and 15 rebounds.
VanDeest and Ben Simons scored 14 apiece.