Alec Burks scored 24 of his game-high 33 in the second half to overcome a 15-point, halftime deficit and a 22-point deficit earlier.
"I was just trying to make play," Burks said.
The Buffs' comeback got started when Burks sparked a 12-0 run, scoring the first nine points before Marcus Relphorde hit a three.
"I was counting on my teammates to make shots," Burks said about Relphorde and others.
The first half was a completely different story for Burks and the Buffs. After gaining an 11-9 lead a few minutes into the game, Texas went on a 16-0 run spanning more than 6 minutes.
J'Covan Brown did most of the damage during the run, scoring eight straight points including two 3-pointers. Brown finished the half with 14 points on 4-for-5 shooting from behind the arc.
"It's not that we were down 15, it's how we were down 15. Not competing," coach Tad Boyle said about his team's effort in the first half.
Colorado was losing rebounds, assists, points in the paint and second chance points after the first half. Texas turned all of that into a 22 point lead with 4:40 remaining in the half.
The comeback started at that point. Colorado went on short 7-0 run to keep it in the game before halftime.
Boyle preached defense, rebounding and offensive execution during halftime in order to get his team back in the game.
"It was the first time I thought we got outplayed significantly in our own building," Boyle said.
The second half started with the same back-and-forth as the first half, but Burks got an and-one drive to drop going into the first TV timeout. Burks came back and a hit the free throw to cut the lead to 14. He followed that up with a dunk, followed by a pair of jumpers.
Relphorde then hit a 3-pointer to cap off the 12-0 run in just 2 minutes 30 seconds. Texas coach Rick Barnes was forced to call a timeout and try to get his team's head back in the game.
Burks came right back at the Longhorns when he grabbed the next rebound and went coast to coast to cut the lead to three with just under 12 minutes remaining. Levi Knutson then came alive. He hit two 3-pointers and a jumper as Burks kept getting to the free-throw line. The Buffs were able to claim the lead and push it all the way up to 11 after Higgins was able to finish at the rim, getting fouled in the process.
With less than 4 minutes left, Texas launched one final comeback. The Longhorns started to attack and get to the free throw line. Tristan Thompson and Cory Joseph got to the line multiple times in the last few minutes, eating away at the lead. Jordan Hamilton was able to get to the rim and finish, even when he was fouled, completing the three-point play. The Buffs fought off the comeback at the free throw line.
Andre Roberson, Higgins and Burks each got to the line to close out the game.
Hamilton hit a three with 18 seconds left in the game to cut the lead to two. After Texas fouled Burks, he went to the line and hit both. Hamilton shot a three from 30 feet, clanking it off the front of the rim. Higgins was fouled as he went to the line with only 3 seconds left. Higgins hit one of two as the Buffs knew the game was over.
The students came sprinting out onto the court to celebrate the victory over the No. 5 team in the country.
"It was crazy with all these people around you," said Burks.
The second half was when the Buffs came to play. Texas leads the Big-12 in rebounding and the Buffs out-rebounded them by 10 in the second half. Colorado also shot 58% from the field while holding Texas to 29%. The Buffs were creating easy shots for each other, having 12 assists with only four turnovers.
Burks 33 points was his second highest output of the season, only topped by his 36 against Missouri to open Big-12 play. Burks was able to get to the line 20 times in the game, hitting only 12 of them. Burks went 7-for-10 from the field in the second half after only hitting three of 11 in the first half. He also grabbed 10 rebounds for his third double-double of the year.
Knutson was able to contribute 21 points off the bench, including three 3-pointers. Andre Roberson also played a key role off the bench. Roberson missed two free throws in the final minute, either of which would have given Roberson his fourth double-double of the season.
Roberson had a game-high 11 rebounds to go with his nine points, five assists and two blocks. His five assists led the Buffs.
Junior Nate Tomlinson started for the first time since coming back from an ankle injury. Tomlinson hit his only shot, a three pointer from the corner. Tomlinson had three assists without turning the ball over, but coach Boyle saw more from Tomlinson than what the box score showed.
"He's that oil that you need for your machine to run," said Boyle. "He makes guys better."
Colorado won back-to-back games for the first time since they opened conference play 3-0.
"Small opportunities lead to big opportunities," said senior Knutson.
This win will get the Buffs back into bubble talks but they need to finish the season strong in order to make the tournament. Colorado needs to keep rolling as it takes on Iowa State in Ames on Wednesday. Colorado closes out the regular season next Saturday at home against Nebraska. It will be the final home game in the Big 12 for Colorado for seniors Higgins, Knutson and Relphorde.