Woodley and West scored the final six points to thwart McNeese State's come-back bid. Woodley, who was 8 of 13 from the field, had 18 points and West had 17 with seven assists and three steals.
The Demons (13-10, 8-4), who have won five of their last six games, were playing without Marvin Frazier, their third leading scorer and top rebounder. He was out with an ankle injury.
Northwestern State trailed 52-47 when West hit a trey to start a 10-2 run and take a 57-53 lead with 9:38 remaining. The Cowboys charged back late to close to 73-72 with 38 seconds left before West made two free throws to seal the win.