Zamal Nixon knocked down four free throws in the final 16 seconds and helped propel Houston to a 64-57 victory on Wednesday night at Hofheinz Pavilion in Houston.
The Cougars (11-6, 3-1), who have won three straight and five of their last six, trailed by two at 55-53 with six minutes left. However, they used a 5-0 flurry to take a 58-55 lead they did not relinquish.
Brown, Thibodeaux, and Harris also scored in double figures for Houston.
Both teams shot less than 40 percent from the floor. The Cougars outscored the Golden Hurricane by ten, 21-11, at the charity stripe.
Tulsa (9-9, 2-2) was led by Justin Hurtt. Hurtt tallied 20 points in the contest. Steven Idlet finished with a double-double, as he posted 14 points and grabbed 12 boards.
Bryson Pope also scored in double figures for Doug Wojcik's club, as he concluded his night with 13 points.