The Cowboys were fueled by forward Le'Bryan Nash, who finished with a game-high 21 points.
OSU had a stranglehold on the game for most of the way, but the Sooners still had their chances late.
When the Cowboys went a stretch of six possessions with five turnovers, OU could only cut the lead from 14 to 11.
A couple more buckets, and the 5-point deficit the Sooners eventually drew within could have been just a one-possession game.
As it was, they closed to 66-61 with 40 seconds to go but could climb no closer.
The Sooners shot very poorly as a team, managing just 32.4 percent to just 38.6 percent for the home team.
OSU shot 10 more free throws than the Sooners and made 10 more (23-for-30).
That proved to be huge.
The two combined for just 13 points on 5-for-20 shooting.
Meanwhile, Cowboys guard Keiton Page didn't shoot the ball all that well himself, making just 5-of-16, but he still finished with 18 points.
Guard Brian Williams was the third Cowboy who scored in double figures with 13.