L.J. Rose added 16 points and Jherrod Stiggers chipped in 15 points for the Cougars (16-14, 8-9 American), who shot 55 percent, including 12 of 23 3-pointers and made 12 of 14 free throws.
The Bulls hit 48 percent from the field but struggled from behind the arc, connecting on 1 of 9, and made 12 of 24 free throws.
With the game tied at 59, Rose hit a jumper to start a 15-3 spurt, capped by two Stiggers' free throws with 52 seconds remaining. Rose had five points in the game-deciding run.
After Houston pushed its lead to 15 to start the half, USF answered with a 12-0 run of its own to cut the Cougars' lead to two on a Brock jumper with 10:47 to go. Chris Perry had five points to lead the run for the Bulls.
The Cougars pushed the lead to eight on a House layup, but USF responded once more with an 8-0 run to tie it at 59 on a John Egbunu layup with 5:33 left.
Houston opened the second half on a 19-6 run to open up a 51-36 lead after two House free throws with 13:33 left. Rose and House each had six points in the spurt.
Houston used a 17-7 run over a 5 1/2 minute stretch of the first half to open up a 22-13 lead on a House 3-pointer. House had eight points, and Brandon Morris had back-to-back 3-pointers to lead the run for the Cougars.
USF took a 30-29 lead with eight seconds left in the half on a Rudd dunk that capped a 9-0 run - seven scored by Rudd. However, Stiggers gave the Cougars a 32-30 lead at the half with a 3-pointer from just inside midcourt that banked in at the buzzer.