Young completed 11-of-18 passes for 161 yards for the Longhorns (3-0), who outgained Rice by a 525-228 margin. Benson gained 169 of his yards in the first half.
Texas junior tight end David Thomas caught four passes for 90 yards and a pair of scores.
Freshman quarterback Joel Armstrong accounted for the Owls' only touchdown with a 44-yard run late in the fourth quarter. Brennan Landry added a pair of field goals as Rice (2-1) saw its five-game win streak come to an end.