Sims scored on a 3-yard run and a 47-yard run that put the Cougars up 28-0 in the third quarter. He would later make a 16-yard run for his third touchdown. David Piland was 26 of 43 for 361 yards and two touchdowns, including a 31-yard pass to Daniel Spencer and a 25-yard pass to Larry McDuffey.
Houston (1-3, 1-0) opened its final season of Conference USA play before moving to the Big East.
Rice (1-4, 0-2) had hoped to rebound from an overtime loss to Marshall.
The win keeps the Bayou Bucket in Houston.