Leading 57-49 with 1:46 left to play, the Cougars just had to hang on for the remaining 106 seconds to even their Conference USA record to 1-1 and improve to 4-10 overall this season.
Last year, in a similar situation, Houston surrendered a 13-point lead in the final 2:57 before suffering an 80-77 heart-wrenching loss to the Blazers.
But, on this second time around, Houston proved more determined and fought off UAB's comeback attempt by hitting some key free throws down the stretch and held on for a 67-65 victory.
Torrence Botts scored a lay-up with 1:04 left to play to give Houston a 62-53 lead. On UAB's ensuing possession, LeAndrew Bass drove the length of the court, but he missed his lay-up attempt. George Williams snatched the rebound, but Sidney Ball was able to reach in for a held ball that gave UAB possession.
The Blazers took advantage of the turnover when Ball hit Eric Batchelor for the three-point field goal on the inbounds pass to cut Houston's lead to 62-56 with 57 seconds left.
On Houston's next possession, the Cougars broke UAB's full-court press and Bass fouled Botts at the half-court line. Botts made one of his two free throws to give Houston a 63-56 lead with 46 seconds left.
UAB drove the ball down the court quickly, and Will Campbell scored on a slam-dunk. Houston tried to throw the ball inbounds, but Chad Hendrick mishandled the inbound pass, and Bass made two free throws to make the score, 63-60, with 38 seconds remaining to play.
Houston turned the ball over again on its next possession and UAB had the ball with 32 seconds needing three points to tie the score.
Bass backed the ball down the right side and spun into the lane to drive towards the basket. But, Dominic Smith beat him to the spot and Bass was called for a charging foul that gave Houston the ball with 25 seconds left.
Batchelor fouled Chad Hendrick, and he made both free throws to give the Cougars a 65-60 lead with 23 seconds remaining.
Tony Johnson made a lay-up on UAB's ensuing possession. With score 65-62 with 17 seconds remaining to play, Dominic Smith made one of his two free throws to give the Cougars a four-point lead. Then, Will Campbell was called for his fifth foul with eight second left. Hendrick made both of his free throws to give the Cougars a 67-62 lead. P.J. Arnold hit a three-pointer from the right wing as the buzzer sounded to make the final score 67-65.
George Williams led Houston with 16 points and eight rebounds, while Hendrick tallied 13 points and Smith added 12. Patrick Okafor also scored 11 points for the Cougars who will play next at Louisville on January 17.