Woodely, who hit 8-of-12 field goals, also had three blocks. West was 5 of 10 from the floor as Northwestern State (16-13, 12-6 Southland) made 50 percent of its field goal attempts.
Northwestern State led throughout most of the second half but ORU stayed close, climbing within four (82-78) following a 3-point shot by Adrion Webber with 37 seconds remaining. West then made four consecutive free throws and Woodely made two more for the win.
The Demons secured a fourth-place finish in conference which will give them a first round bye in the conference tournament, beginning March 12.
Brison White added 14 points and DeQuan Hicks had 11 for the Demons.
Shawn Glover had 26 points and Korey Billbury added 21 for ORU (16-15, 10-8).