After SE Lousiana closed within 80-77 with 3:04 left, White made a free throw and Woodley followed with a jumper to extend the Northwestern State (13-13, 9-6 Southland Conference) lead to six.
The teams traded baskets and Dre Evens pulled the Lions (11-15, 6-9) within 85-81 with 34 seconds left, but Jalan West made both free throws to make it 87-81 and secure the win for the Demons.
West and DeQuan Hicks scored 11 apiece for Northwestern State which shot 34 for 62 (54.8 percent) from the field.
Evans was 6 of 11 from 3-point range with 26 points and five assists for SE Louisiana. The Lions trailed 70-54 before going on a 12-0 run to cut the gap down to four with 6:44 to play.