Erik Thomas had 14 points and 10 rebounds, Tevin Broyles had 13 points, and Travin Thibodeaux had 12 for New Orleans (6-12, 2-5 Southland), which snapped a five-game losing streak and won its first conference game in over three weeks.
Central Arkansas had a 20-9 run early in the second half, capped by a Jordan Howard 3, which gave the Bears a 68-57 lead.
The Privateers stormed back, putting together a 22-4 scoring stretch highlighted by a Kevin Hill dunk and a Christavious Gill 3-pointer, which gave them a 78-72 advantage with 5:20 to go.
New Orleans held the lead the rest of the way, and another Hill dunk with 1:55 left pushed the lead to 10.
Howard made a career-high seven 3-pointers and scored 25 for the Bears (3-14, 2-5).