Bowling Green trailed 44-41 with 2:32 left in the second half when Eastern Michigan's Derek Thompson made a free throw. A'uston Calhoun made a layup and Crawford knocked down the game-winning shot for the Falcons (6-9, 1-1 Mid-American Conference).
Thompson attempted a 3-pointer the Eagles (7-9, 0-2), but it missed and sealed the victory for Bowling Green -- which snapped a five-game losing streak.
Calhoun finished with 17 points and Crawford scored 11 points on 4 of 16 shooting and nine turnovers for the Falcons.
Thompson was the only Eastern Michigan player to score in double figures with 11 points. Jamell Harris finished with 11 rebounds and Da'Shonte Riley had 10 boards.
The Eagles have lost four straight.