Dillard scored his second touchdown on a 3-yard run late in the third to give Rice (7-4, 5-2 Conference USA) a 24-13 lead. Hull caught Driphus Jackson's 5-yard TD pass with 5:41 left to cap the scoring.
Jackson finished 10 of 22 for 227 yards, two touchdowns and an interception. He also ran for 53 yards on 11 carries.
The Owls went 82 yards on four plays on their opening drive of the second half, taking a 17-3 lead on Jackson's 24-yard touchdown pass to Jordan Taylor.