The Cougars gained control of the game early as they held the Horned Frogs scoreless for the first nine minutes of the game and jumped out to a 12-0 lead.
Truscott led Houston to a 33-20 halftime lead as he scored 11 points and grabbed 11 rebounds in the opening period. Jarrett Sidney scored eight points and Andre Owens added five points in the first half.
The Horned Frogs opened the second half with a 6-2 run to close to within 35-26. But, that was as close as they could get as Truscott slammed home a backdoor lay-up and Sidney hit Jeremee McGuire for a lay-up off a fast break. McGuire also was fouled by Jamal Brown and hit his free throw to give the Cougars a 40-26 lead.
The Horned Frogs didn't get any closer until Bingo Merriex hit a three-pointer from the top of the key to help TCU pull within seven, 57-50, with 1:29 left to play. But, once again, Truscott answered as he nailed a pair of free throws with 38 seconds remaining.
Sidney finished the game hitting two free throws with seven-tenths of a second left to finish with a career-high 10 points and make the final score, 61-56.
The victory moves Houston into a first-place tie with UAB in Conference USA's National Division with a 4-2 league record. The victory was the Cougars' third straight win and improves Houston's overall record to 6-11.
UH returns home to play Tulane in a C-USA game on Tuesday, February 4 at 7:30 p.m. in Hofheinz Pavilion.