Jordin Williams buried a 3 for LSU-Alexandria with 22 seconds left to cut McNeese State's lead to 73-72. Williams then fouled Shaun Johnson who calmly sank two free throws with 16 seconds remaining for a three-point lead.
DeAngelo Coleman missed a 3, and Burr was fouled with a second left and converted two free throws for the final margin.
Craig McFerrin had 19 points, on 7-for-11 shooting, 11 rebounds and three blocks for McNeese State (2-7).
Brian Sylvester had 22 points, 15 rebounds and six blocks for LSU-Alexandria.
The Generals led 33-31 at halftime but went without a field goal for three-plus minutes and trailed 55-47. McFerrin made McNeese State's final field goal at the 3:21 mark but the Cowboys made 12 of 16 free throws the rest of the way.