Houston shot 53.8 percent (35 of 65) from the floor and made 11 of its 18 attempts from 3-point range. The Cougars enjoyed a 52-25 rebounding advantage.
Young had seven points and Harris six during a 19-5 run over a 5:15 second-half stretch that gave Houston permanent control. A dunk by Thomas ended the surge and gave the Cougars a 70-50 lead with 10:04 remaining.
Colorado State graduate transfer John Gillon has chosen Syracuse, giving the Orange a potential starter at point guard entering the 2016-17 season.
DeSean Murray, who averaged 20.2 points as a sophomore at Presbyterian, will transfer to Auburn to play for coach Bruce Pearl.
Former Kentucky guard Ed Davender, the only Wildcat with at least 1,500 points and 400 assists, has died. He was 49.