Memphis (4-1) took its first lead of the game with 1:43 left in the third quarter when Geoffrey Cantin-Arku blocked a field goal and returned it 80 yards.
Memphis went ahead 28-17 with 11:16 remaining in the fourth after a five-play, 88-yard drive ended in Henigan's 59-yard connection with Demeer Blankumsee. Watson made it 35-25 with 2:16 left on a 1-yard score.
Boise State got a touchdown and two-point conversion when Ashton Jeanty caught a 7-yard pass from Maddux Madsen with 39 seconds remaining. Jeanty scored all four of Boise State's touchdowns — two rushing and two receiving.
Roc Taylor joined Blankumsee with a touchdown grab for Memphis. Taylor caught five passes for 102 yards and Blankumsee added 83 yards. Henigan added 64 yards on the ground on 13 carries.
Madsen completed 11 of 14 for 175 yards and two touchdowns for Boise State (2-3).
------ AP college football: https://apnews.com/hub/college-football and https://apnews.com/hub/ap-top-25-college-football-poll