The victory sends the Longhorns into Sunday's regional final against Memphis, who routed Michigan State 92-74.
Whoever Texas next faces can expect as much burnt orange -- if not more -- in the stands when the Longhorns get a chance to reach the Final Four for the first time since 2003.
Mixing their inside and outside games, the Longhorns (31-6) took control early. Still, they were up only 52-51 after Lopez did everything but dribble the ball up the court to rally the Cardinal (28-8).
Texas answered with a 20-3 run, punctuated by several plays that sent the heavily pro-Longhorns fans to their feet. Most were by Augustin, but Pittman also contributed by using his girth to throw Lopez off stride.
Lopez was so frustrated that on one play he was trying to signal officials to call three seconds on the humongous guy while also trying to play defense.
Lopez had 24 of Stanford's first 48 points, but finished with 26 and 10 rebounds.
As the final seconds ticked off, he pounded a fist on the floor and untucked his shirt, scowling as he walked to midcourt for the postgame handshake.
The Cardinal already were on their deepest run since 2001. Whether they can get back next year might depend on whether Lopez and his 7-foot twin brother, Robin, stick around for their junior years.
They'll need more scorers, too, as reserve Landry Fields had the second-most points with 11. No one else had more than six.
Augustin, playing before lots of family in his adopted hometown, had 23 points, seven assists and five rebounds. He scored eight points during the game-breaking run and everyone knew this one was over when he fed Damion James for a dunk so electrifying that he began celebrating on his way down.
James scored 18 points. A.J. Abrams, Texas' shooting ace the first two games, had only 12 on 5-of-14 shooting. He was only 2-of-8 on 3-pointers.
The Longhorns also got 10 from Connor Atchley, one of six big men who logged time trying to cover Brook Lopez. The most effective, though, was Pittman, a sophomore who arrived in Austin weighing 366 pounds and in need of a rebuilt body if he was ever going to play.
Pittman wound up being the first sub coach Rick Barnes asked to slow Lopez. Barnes deployed all four of his reserves 6-foot-7 or bigger early one. He knew he had a lot of fouls to use -- and the guys seemed intent on using them. The Cardinal took nine free throws before the Longhorns even had one.
There's no doubt Pittman was the most effective. While he produced only four points and six rebounds, the best stat might be this: Lopez's last field goal came with 13:55 left. Pittman didn't cover him that entire time, but he certainly wore down Lopez and frustrated the heck out of him.
Stanford had nowhere else to go for offense. The Cardinal had back-to-back turnovers on two second-half possessions Lopez sat out, so coach Trent Johnson called a timeout to get him back in.
The Cardinal made only five of their first 21 shots, and three of those were by Brook Lopez. The game was 17:29 old before they finally hit anything longer than an 8-footer.
At the half, their starting backcourt was 1-of-9; the only basket was a 3-pointer in the final seconds. Another 3 to open the second half provided some hope, but the Longhorns were just too deep.