Brett Hundley, a redshirt freshman, was 21 of 28 for 202 yards and two touchdowns and rushed for 68 yards and a touchdown.
Franklin just missed his career high of 216 yards rushing set in 2010 against Washington State. He became the first player in UCLA history to have two rushes of at least 72 yards in a game after scoring on touchdown runs of 74 and 78 yards in the first half.
Rice's Taylor McHargue threw for 172 yards and two touchdowns on 17 of 28 passing and rushed for 95 yards and a touchdown on 22 carries.
UCLA finished with 651 total yards in Jim Mora Jr.'s first game as coach, compared to 347 for Rice.