Ex-Texas A&M quarterback Kyle Allen threw for 225 yards and a touchdown but was intercepted twice in his first game for Houston and the Cougars had to hold on to beat Arizona 19-16 in their week-delayed season opener on Saturday night.
Houston (1-0) gave Major Applewhite a victory in his head coaching debut a week after the scheduled opener at UTSA was canceled due to Hurricane Harvey.
John Leday's 81-yard kickoff return set up Houston's go-ahead touchdown with 45 seconds left in the first half.
Josh Pollack kicked three field goals for Arizona (1-1), the last, from 42, yards cut the lead to 19-16 with 8:32 to play.