After committing two fouls in the first five minutes of the game, Woodard was held scoreless in the first half, playing only five of the first 20 minutes. Oklahoma connected on 10 of 15 3-pointers in the first half and held a 43-39 halftime lead but trailed for most of the second half.
Javan Felix, who scored a career-high 28 points for Texas (11-3, 0-1 Big 12), hit a pair of free throws after Isaiah Cousins was ejected for throwing an elbow to tie the game at 78 with 2:20 remaining. But Woodard answered with four straight points—two from the free throw line with 1:53 left and two more on a layup with 1:08 remaining to put Oklahoma (12-2, 1-0) up for good.
"I was dealing with foul trouble at the beginning of the game but my teammates and coaches encouraged me to stay locked in," Woodard said. "The last few minutes of the ballgame, Coach kept calling my number. I just wanted to make the right plays for my teammates."
Woodard knocked down 6 consecutive free throws in the final minute before missing two straight with 15 seconds left, giving Texas a chance to tie the game. A potentially game-tying 3-pointer by Damarcus Croaker was off the mark, allowing the Sooners to snap an eight-game losing streak in Austin.
"When you get a little bit of a lead in that last minute, it's hard to finish the game. It's hard to get a win," Oklahoma head coach Lon Kruger said. "Texas has been playing great, so to come into a tough place and beat a good team that's playing well, I feel awfully happy for our guys."
Texas, who did not attempt a free throw in the first half, opened the second half on a 10-2 run. Felix scored the first six points of a separate 8-0 run that gave the Longhorns their largest lead at 67-59 following a pair of free throws by Cameron Ridley with 9:34 left.
But, as Oklahoma was chipping away at Texas' lead, Felix and Ridley each missed two free throws with 2:53 remaining with the Longhorns holding a 76-75 advantage.
"That's unacceptable on my part," Felix said. "That was definitely a big part of the game. We can't let that happen again. It definitely hurt us going down the stretch."
Buddy Hield's fourth 3-pointer of the game put Oklahoma ahead, 78-76, with 2:20 left before Cousins was called for his second technical foul of the night.
"Anytime along the way if you lose, you always felt you let one get away," Texas head coach Rick Barnes said. "If they didn't know it, because we've certainly talked enough about it, they will know now that there is a difference in level of play right now."
Cameron Clark entered the game averaging a Big 12-best 18.5 points per game but was limited to eight points on 1-of-9 shooting. Hield led Oklahoma with 22 points while Cousins and Tyler Neal each chipped in 13 points to go along with Ryan Spangler's 11.
Cousins, Hield, Neal and Frank Booker all hit at least three shots from beyond the arc in the victory, helping the Sooners tie a season high with 13 3-pointers. That helped them overcome being outscored 42-20 in the paint.
"Cam's been so consistent for us. he couldn't get anything going offensively," Kruger said. "I probably wouldn't have thought our chances would have been very good if you would have told me those stats beforehand."
Felix connected on just 2 of his last 9 shots from the floor after starting 8 of 10 from the field. The Longhorns also got a career-high 15 points from Croaker, who hit 5 of 8 attempts from beyond the arc.
Oklahoma avoided losing consecutive games for the first time this year despite being outscored 42-20 in the paint. The Sooners face No. 16 Kansas in their Big 12 home opener Wednesday while Texas takes on No. 6 Oklahoma State in its Big 12 road opener.