J'Covan Brown's three-point play with 36 65, in the quarterfinals of the Big 12 tournament.
With the game tied at 65, Brown made a spinning move into the lane, drew the contact and finished the shot. The ensuing free throw gave Texas a three-point lead it would not relinquish.
Brown finished with a game-high 23 points to pace the Longhorns (20-12). Myck Kabongo added 11 and Clint Chapman chipped in 10 points and eight rebounds as the Longhorns bolstered their NCAA resume with a win over a ranked opponent.
Texas, seeded sixth, advances to Friday's semifinal where it will face Missouri, which cruised to an 88-70 win over Oklahoma State earlier on Thursday.
"I told our guys right after the game that I've coached a lot of basketball games and we've had a lot of different teams, but I'm not sure we're any more proud of the effort these guys gave tonight," said Texas head coach Rick Barnes after the victory. "I thought we stayed with our game plan from start to finish better than any point the entire year."
Royce White contributed a double-double with 17 points and 10 rebounds for third-seeded Iowa State (22-10). Scott Christopherson, Percy Gibson and Melvin Ejim scored 10 points apiece in the loss.
After Brown's three-point play, Jonathan Holmes came up with a steal on a White turnover and buried both at the line to make it a five-point contest with under 30 seconds to play.
Iowa State still had life, but Chris Allen dribbled the ball out of bounds off his foot with under ten seconds to play and Kabongo went 1-of-2 from the line to give Texas a 71-65 lead with 7.9 seconds remaining.
"It was disappointing to go out in the first round, especially with all the fans we had in attendance," said Iowa State head coach Fred Hoiberg. "They made big plays and I thought we put our heads down a little bit as team. Then we regrouped and found a way to get back in the game, but they made big plays down the stretch and we didn't."
Trailing by 11 early in the second half, Texas reeled off a 22-4 run in a five-plus minute stretch as Kabongo's three-pointer gave the Longhorns a 51-44 lead with 11:19 to play.
The Cyclones battled back with a 15-8 spurt, as Chris Babbs' free throws tied the game at 59.
Texas would score the next six, but Iowa State answered with six of its own, capped by White's tough layup to knot the game at 65 with 52 seconds left in regulation, leading to the decisive three-point play from Brown.
Iowa State took the largest lead of the first half at nine when Bubu Palo and Babb connected on back-to-back threes to give the Cyclones a 28-19 edge, but Texas closed the half on a 6-1 run to cut the deficit to 29-25 at the break.
Texas struggled from three-point range, connecting on 3-of-15 (20 percent). Iowa State faired slightly better as it made 5-of-18 (27.8 percent) from beyond the arc... Iowa State turned the ball over 14 times compared to just five turnovers for the Longhorns.