Gary Johnson tied a career high with 15 points for the Longhorns, who held Iowa State to three points in overtime. Texas continues to show a knack for digging out of its own holes, rallying from double-digit deficits to win its last three games.
The Longhorns (19-4, 6-2 Big 12) pulled this one off despite an off night from Augustin, who was 5-of-22 from the floor. But his overtime jumper gave the Longhorns a 66-62 lead that they expanded at the free throw line, and Justin Mason's layup sealed the win.
"He stayed with it, and I told him in the locker room, 'You missed a bunch but you made the big one,"' Texas coach Rick Barnes said of Augustin.
Jiri Hubalek had 24 points to lead Iowa State (13-11, 3-6), which lost its ninth straight against ranked opponents. Wesley Johnson scored 10 on 4-of-17 shooting.
The Cyclones were just 1-of-9 from the floor in overtime, their only make coming on a Diante Garrett 3 with 14 seconds left. Iowa State has lost five of six after an encouraging start to the conference schedule.
"It's a disappointing loss," said Cyclones coach Greg McDermott, who is 0-8 against Top 25 teams in two seasons with Iowa State. "I don't think anyone is into moral victories in our locker room, and that's a good thing."
With 56 seconds left in regulation, Abrams was knocked to the floor by Rahshon Clark and hit two free throws for a 62-60 lead. The Cyclones then caught a break when Hubalek was fouled on the wing, and he hit two from the line to tie the game at 62.
Abrams, who was 7-of-10 from 3-point range, front-rimmed a jumper as the buzzer sounded.
Texas fell behind by as many as 13 early in the second half, but the Longhorns chipped away at the lead. Abrams hit a 3 with 6:53 left in regulation to make it 53-49, Johnson hit two free throws make it 55-53, and Augustin added two more to tie the game at 55 with 4:21 left.
Augustin then buried a floater in the paint to give Texas its first lead of the second half, 60-58.
He spent most of the game forcing up tough shots. But Augustin, the Big 12's second-leading scorer, hit all six of his free throws and the jumper that gave Texas a lead late in regulation.
"You're going to miss shots. That's part of the game," he said. "You have to keep playing. You have to be aggressive."
Iowa State pushed a four-point halftime lead to 42-29 just four minutes into the second half. Johnson kicked it off with a wide-open 3, and Hubalek added a pair of tough inside baskets and four free throws to give the Cyclones their largest lead.
Abrams and Augustin hit 3s to bring Texas within 44-37.
Iowa State held Texas to 31.4 percent shooting in the first half and led 31-27 at the break.
The Cyclones went on a 15-6 run, capped by Clark's 3, to take a 19-14 lead midway through the first half. Abrams hit a pair of 3s to tie the game at 20, and buried his third of the half to make it 27-all.
Damion James had eight points and 14 rebounds for Texas, which has won three straight against the Cyclones. Clark tied a career high with 14 boards for Iowa State.
"A loss is a loss. We might have been close, but we didn't get it done," Hubalek said. "We got some good looks, but we just didn't make the shots."
Iowa State had struggled mightily against ranked opponents this season, losing to Kansas, Kansas State and Texas A&M by an average of 22.3 points. Perhaps Texas was looking forward to a big game of its own, a home date with No. 4 Kansas on Monday.
That one could have major ramifications on the Big 12 race. If Augustin can play like he did down the stretch on Saturday, Kansas could have its hands full.
"There is none better," Barnes said of Augustin. "On nights when he's not shooting it, he affects the game in a lot of different ways, and he did here."
Iowa State's student section and band was clad in pink T-shirts and the Cyclones wore pink shoelaces to help promote breast cancer awareness. Both Barnes' and McDermott's wives are breast cancer survivors.
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