Lammert made a big 3-pointer early in the run, a shot that came after Hield missed a potential dagger 3-point attempt for the Sooners.
Isaiah Taylor scored 18 points for the Longhorns and started the big run with a three-point play. Lammert and Javan Felix scored 14 points each for the Longhorns (19-10, 10-6).
Oklahoma coach Lon Kruger called the final minutes "a blur" as the Longhorns romped by making tough shots, forcing turnovers and grabbing seemingly every long rebound. Texas outrebounded Oklahoma 43-31 and the gap grew dramatically in the final minutes.
"We didn't have too many good possessions the last 4 or 5 minutes," Kruger said. "They whipped us pretty good on the boards, especially late."
Texas trailed 58-51 before Taylor converted his three-point play to start the run, which really took off when Lammert's 3-pointer energized the home crowd. Hield tried to shoot the Sooners (22-6, 10-6) back in it but missed another 3-point attempt. The Sooners went scoreless for 7 minutes as the Longhorns broke the game open.
"We need to be more poised," said Hield, who reached 30 points for the ninth time this season. "It's a game we'll learn from."
Hield beat Texas in the first matchup with a 3-pointer in the final seconds and lit up the Longhorns again with 23 points in a wide open first half.
Hield scored from everywhere early. His opening basket was a twisting, baseline drive for a layup, and he followed that with four 3-pointers and a dunk of an alley-oop pass. He was on pace to match his career-high of 46 points scored in Oklahoma's triple-overtime loss to Kansas in January.
But even with Hield scoring at will, the Longhorns kept up with the Sooners at nearly every turn. The Longhorns shot 50 percent in the first half and Taylor's layup in the final seconds pulled Texas within 40-37.
"The goal wasn't to 'hold on,'" Felix said. "It was to keep getting stops and take good shots."
Jordan Woodard made two 3-pointers for Oklahoma early in the second half and Hield managed just one shot — a made 3-pointer — over the first 8 minutes of the second as scoring by both teams tapered off. Hield's 3-pointer put the Sooners up 52-45 but the Longhorns kept counterpunching to keep Oklahoma from pulling away.
Once they caught up, the Longhorns rolled over the Sooners as the points piled up quickly.
"Our guys were able to dig deep," Texas coach Shaka Smart said. "Our guys didn't get down, didn't get bummed out."
Oklahoma: Hield, the national leader in 3-pointers made per game, made six against Texas and needs four more to set the Big 12 season record.
Texas: The Longhorns countered Hield's big game with better balance. Texas had five players score in double figures with Kerwin Roach, Jr., scoring 12 and Eric Davis Jr., adding 10.
"They have a lot of weapons," Kruger said. "It all starts with Taylor."
Smart said he had to make a big defensive switch on Hield just before Texas made its big run.
"We said we had to get two guys on (him) every time he touched the ball," Smart said. "He's something else."
That also meant defenders would have to be just as quick switching back to cover whoever else had the ball.
"Our guys had great composure. Great focus," Smart said.
Oklahoma hosts No. 19 Baylor on Tuesday.
Texas hosts No. 2 Kansas on Monday.