But Temple's Kee-ay Griffin scored on a 21-yard run, Bruce Francis caught a 32-yard TD pass and Travis Shelton returned the second half kickoff 92 yards to put the Owls (3-7, 2-4) ahead 24-21.
Edelman ran for his third touchdown then threw a 7-yard score to Sam Kirkland to put Kent State back in front, then a 21-yard field goal by Reed made it 38-31 early in the fourth.
Temple quarterback Adam DiMichele's third touchdown pass, a 51-yarder to Jason Harper, tied it with 10 minutes left. But an eight-play, 60-yard drive on Kent State's next possession set the stage for Reed's winning kick.
Eugene Jarvis rushed for 185 yards and a touchdown for the Golden Flashes.
DiMichele was 17 of 29 for 282 yards, with one interception. His favorite target, Harper, caught 10 passes for 209 yards and two touchdowns.