Texas trailed 41-28 early in the second half before Abrams hit a 3-pointer, then converted a 3-point play. The Longhorns roared to the lead behind a 24-6 run that ended the Buffaloes' hopes of an upset. Abrams finished with 17 points and four 3-pointers.
Richard Roby scored 18 points for Colorado (9-8, 1-2), which hit seven 3-pointers in the first half, but none in the second.
Even with Texas' big rally, Colorado nearly clawed its way back at the end. The Longhorns led 62-50 midway through the second before the Buffaloes started chipping away.
Colorado's last chance came when the Buffaloes forced shot a clock violation with 18 seconds left, but Roby missed a 3-pointer before Levi Knutson's tip-in at the buzzer.
Texas struggled to score in the first half after wingman Damion James, the Longhorns most consistent scorer of late, went to the bench six minutes in with his second foul.
Colorado, a 35-percent 3-point shooting team, went 7-of-13 from the floor in the first half and led 37-28 at the break. Augustin scored 14 in the half but Texas hit just one field goal over the final 5:30.
Colorado quickly pushed the lead to 13 with a pair of layups before a 10-0 Texas run over then next 90 seconds.
Abrams made a 3-pointer then converted a 3-point play, James made his first basket, and Connor Atchley started a fast break with a steal and finished it with a putback off James' missed dunk to pull with 41-38.
After a Colorado timeout, Justin Mason hit a layup and Abrams finished the rally with a steal and pulled up on the fast break for a 3-pointer, punctuating the swish with a furious yell and a 43-41 Texas lead, it's first of the game.
Justin Mason blocked shots on the Buffaloes' next two possessions and had a steal that led to another basket and Texas built its lead to six.
Colorado looked stunned when Abrams drilled yet another 3-pointer from deep in the left corner to finish the 24-6 run.
Still, Texas nearly wasted the effort when the offense went into a late funk. Atchley's 3-point play with 4:25 to play put Texas up 69-59 but it was the Longhorns' last basket of the game.
A jumper by Roby and a layup by Marcus Hall cut the lead to four and good defense gave Colorado the final chance it couldn't convert.
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