JD Tisdale's dunk put Bowling Green ahead 64-52 with 2:04 left but the Falcons went cold from the line, making 9 of 14.
Derek Jackson's basket got Kent State within 69-66 with 30 seconds left. Then Clarke made four straight free throws to seal it.
Kris Brewer had 14 points for Kent State (15-13, 6-9) and Devareaux Manley had 11. The Golden Flashes were held to 34.9 percent shooting and were outrebounded 44-31.
Kent State won the previous matchup two weeks ago when Manley hit a game-winning 3-pointer with 0.9 remaining for a 62-61 victory.