The Falcons (12-12, 7-3 Mid-American Conference) led 64-56 with 27 seconds left to play before a layup from Malik Perry, a 3-pointer from Tyrae Robinson and a free throw from Jarrod Jones cut the Cardinals' deficit to 65-62 with 6 seconds on the clock.
Perry added a layup for Ball State (14-9, 6-4) as time expired, but Bowling Green held on for the one-point victory.
Jones finished with 15 points and 14 rebounds for the Cardinals, who have lost five out of six. Perry added 11 rebounds and 10 points, while Robinson chipped in with 12 points.
Jordan Crawford scored 10 points and was the only other player in double figures for Bowling Green, which finished 25 of 58 from the field (43.1 percent).