"That's what got us to a point in the season where we were undefeated," said Johnson, who scored a career-high 22 points. "We just got to get back to that point."
The Longhorns (21-6, 7-5 Big 12) led by 13 points in the second half then held off a late-game surge by Nick Okorie, who scored 11 straight points for the Red Raiders to pull them within 69-67 with 58 seconds remaining in the game.
J'Covan Brown made two free throws with 4 seconds remaining to seal the win.
Okorie finished with 21 points for the Red Raiders (16-10, 4-8).
Damion James added 12 points and 10 rebounds for Texas, which had lost six of nine games since moving to No. 1 for the first time in school history.
Texas coach Rick Barnes said Johnson's play was key, especially going 8 of 10 from the free throw line.
"It was huge today and we really survived here against a team that showed a lot of heart," he said. "Even at the end of the game we were wanting to go to him because he's doing the things that at the end of the game that you want -- to go to the guy and he's got to knock down free throws."
Jon Roberson, the Red Raiders' second-leading scorer who injured a rib in the loss at Baylor last week, was held to two points in 27 minutes.
"We just wanted to see if he could play," Tech coach Pat Knight said. "Obviously, it didn't look like he could play so we didn't play him a whole lot. there wasn't much we could do about it."
Okorie started his 11-point spurt with Texas leading 67-56. He made two layups and a 3-pointer to pull Texas Tech within 67-63 with 2:49 remaining. James answered with a basket and Okorie's three-point play with 1:54 remaining made it 69-66 and was Texas center Dexter Pittman's fifth foul.
Texas turned it over and Okorie missed his next shot but was fouled. He made the front end of a 1-and-1 to make 69-67 with just under a minute remaining.
Okorie fouled James and he missed both his free throws. Okorie missed a jumper before D'wayln Roberts fouled Brown, who made both free throws.
Guard Justin Mason said Texas players wanted to get a stop on Okorie.
"I think that's the most important thing," said Mason, who finished with eight points, five assists and two steals. "We feel like when we play our hardest and we play together as a team we have a chance to win. We put ourselves in a bind towards the end of the game by not getting stops and not scoring on the offensive end. But all together, we came out with a win."
Pittman, who left the game for about 5 minutes in the first half after James inadvertently hit him in the head under Texas' basket, scored the Longhorns' first five points of the second half.
Up 47-39, Texas got a six-point spurt within as many seconds. Pittman got fouled by Darko Cohadarevic and officials called it intentional.
Knight erupted off the bench, went out on the court and was hit with a technical foul. Brown hit both free throws for the technical, Pittman made his two and Avery Bradley had a tip-in on the Longhorns' retaining possession because of the technical.
Knight said it was tough to pull close after Texas "jumped on" his team early.
"Our kids just didn't quit and battled all the way to the end," he said. "I kept telling them 'if you hang around good things can happen.' We just need to take this type of effort and get a couple of guys going and just try to finish this next month out."
Texas pulled the Red Raiders defense away from the basket early in the game, hitting 5 of 9 from 3-point range in the first 7 minutes. The Longhorns didn't try another 3 the rest of the first half. They scored 18 points in the paint and led 37-30 at halftime.
Texas lost starting guard Dogus Balbay for the game early in the first half. He appeared to slip and injure his left knee before being called for traveling. He did not put any weight on the leg as he was helped off the court.
"I think it's pretty serious, but we don't know," Barnes said. "He's torn the other ACL back in his first year and we know how tough he is but I'll be surprised if we get good news on it."