For Oklahoma, it was a disappointing way to enter Big 12 play. The Sooners (11-2) start conference play Saturday at Texas.
"We've got to learn from it," Sooners coach Lon Kruger said. "We have to work a lot harder defensively."
Louisiana Tech seemingly had the game sealed in regulation after Woodard's missed 3-pointer with less than four seconds remaining.
But Clark scooped up the rebound, sprinted behind the 3-point line in the corner, turned and fired in a 3-pointer at the buzzer to send the game to overtime.
"I thought about going for two but then I went to the 3-point line and was able to knock it down," Clark said.
Just moments earlier, Clark had a chance to tie the game at the free-throw line before missing the first of two.
Clark finished with 26 points.
Ryan Spangler tied his season highs in points (20) and rebounds (13) before fouling out in the final moments of overtime.
"Obviously it wasn't good enough," Spangler said. "We got the loss. There are things that I need to work on; it doesn't matter what the stats say. I can always get more rebounds, help my guards when they need it. I struggled with that today."
The Sooners lead hovered around double digits for much of the first half.
Oklahoma led by 14 points after freshman walk-on Austin Mankin hit a 3-pointer with 4:18 remaining in the first half.
But the Bulldogs closed the half with a 16-2 run that included three 3-pointers, two by Johnson.
"It's simply making a couple shots, converting from two and from three, and that allowed us to set our press, create a couple of turnovers and then it became a competitive game," White said. "Because it could've been ugly early."
The Sooners didn't lead in the second half past the 7:30 mark and trailed by as many as seven before Clark's heroics helped send the game to overtime.
"As deflated as I was, I can't imagine how deflated our guys were," White said. "To regroup and play with the amount of mental toughness as they did in the extra period was really impressive."