During the 20-7 Oklahoma run to start the second half, Woodard drove the baseline, then found Isaiah Cousins at the 3-point line past a collapsing defense. Cousins nailed the shot to put the Sooners up five.
All of Woodard's seven points came in a seven-minute span in the second.
“He made some really good plays down the stretch not just in terms of scoring but driving and kicking,” Kruger said. “He's tough off the dribble. He gets to the paint and still has good vision and makes pretty good plays.
Iowa State guard DeAndre Kane suffered an ankle injury in the game's final minute.
Kane, who led the Cyclones with 23 points, appeared to come down on an Oklahoma player's foot as Kane went toward the basket.
Kane was helped to the bench by teammates and then again carried off the floor to the tunnel before hopping to the trainer's room after the game.
Kane's injury is not believed to be serious.
Oklahoma will hit the road next week for a pair of Big 12 games.
The Sooners start out at Kansas State (12-4, 2-1) at 6 p.m. Wednesday (ESPN2), then travel to Baylor on Saturday.