Stephen F. Austin (2-3) took a seven-point lead, 59-52 on Demetrious Floyd's 3-pointer with 3:41 left, but it was the final points the Lumberjacks would score in the game.
Melvin Frazier got to the rim for a layup and Cameron Reynolds added a pair of free throws with 1:43 left and Jernard Jarreau added a layup with 1:12 to go to make it a one-point game, 59-58. Osetkowski grabbed the rebound after Kain Harris missed a jumper with 21 seconds left and scored the game winner.
The win was the second in three tournament games for the Green Wave (3-3), who were led by Harris and Louis Dabney, who each had 14 points.
Clide Geffrard scored 20 points for Stephen F. Austin.