Oklahoma (12-2, 1-0 Big 12) returns home to take on Kansas at 6 p.m. Wednesday.
Woodard, who had shot 46 free throws in the four games before Saturday’s win, was having a tough night before the final stretch.
He was in foul trouble from early after picking up two fouls in the first five minutes and even when he was in the game, Woodard was out of rhythm.
Woodard was just 1 for 3 from the floor with no free-throw tries in the game’s first 38 minutes before taking over to end it.
“Obviously we need him in the ballgame — getting to the paint, getting to the rim and making plays for others,” Kruger said. “Good to see him go to the line there late and knock down some free throws.”
Hield led the Sooners with 22 points, while Isaiah Cousins and Tyler Neal added 13 and Woodard 12.
The Sooners, despite Texas’ significant size advantage inside, out-rebounded the Longhorns 39-28.
Oklahoma struggled to contain Javan Felix, who had a career-best 28 points to lead the Longhorns (11-3, 0-1).
But it wasn’t Felix shooting at the end when Texas had one last try.
After Woodard missed a pair of free throws to with 14 seconds left to give the Longhorns another try, Demarcus Croaker’s 3-pointer was off the mark and Woodard came up with the rebound with the help of the possession arrow to seal the win.