Derrius Vick was 18 of 24 for 262 yards with two touchdowns for the Bobcats, with both going to Landon Smith in the first half.
Kent State trailed 14-7 for much of the game, but stayed in reach as Ohio fumbled on their first four possessions in the second half.
After a Dorian Brown fumble, Colin Reardon led the Golden Flashes on an 11-play 78 yard drive, capped by a 25-yard touchdown pass to Chris Humphrey with 4:05 left.
The Bobcats responded as A.J. Ouellette had all six of his rushes for 29 yards on the final drive. Vick added a key third-down conversion with a 7-yard run to get inside the 30, setting up Yazdani's game-winner three plays later.