The victory gave North Dakota State (23-6, 16-2) the Summit League Conference regular season championship.
The Bison took the lead for good at 70-69 with 34.9 seconds remaining when Woodside hit two free throws. The Golden Eagles (16-14, 14-4) had led most of the game, and had reclaimed the lead at 69-68 with 41.3 seconds left on a 10-foot floater in the lane by Dominique Morrison.
After Woodside's free throws, Morrison missed a floater, and Woodside was fouled with 11.3 seconds remaining after Oral Roberts stepped out of bounds with the loose ball off a rebound.
Woodside made five of his next six free throws down the stretch to ice the game.
Robert Jarvis scored 16 of his team-high 23 points for Oral Roberts in the first half.