For the game, Oklahoma converted 11 Texas Tech turnovers into 14 points while giving the ball up seven times, tying a season low.
The Red Raiders had just three points off Sooner giveaways.
In addition to Woodard's two steals, Buddy Hield added a pair.
The Sooners get just one day off before returning for the first Bedlam meeting of the season, at 8 p.m. Monday at Lloyd Noble Center. Oklahoma State hasn't won in Norman since 2004.
Ryan Spangler had 10 rebounds, registering in double figures for the 11th time. Spangler was just 2 of 6 from the field, shooting less than 50 percent for the first time this season. … The Sooners never trailed and the game was only tied once after the initial basket — at 2-2 for 15 seconds before Isaiah Cousins gave the Sooners the lead for good just 1:30 into the game. … The Sooners' last eight games have been decided by single digits. … Hield has led the Sooners in scoring in five of their seven Big 12 games. … The Sooners shot 50 percent from the field for the first time in 13 games.