Buffalo's Mitchell Watt sent the game into double overtime on his layup with 2 seconds left. The Bulls took a 71-69 lead in the second OT when Bryon Mulkey made a jumper with 3:54 to play.
But Buffalo was held scoreless the rest of the way by the Falcons (6-9, 1-0 Mid-American Conference), who have won four straight games. Luke Kraus tied the game at 71-71 with 2:35 left for Bowling Green, and then McElroy later followed with his go-ahead basket.
A'uston Calhoun led the Falcons with 20 points and nine rebounds. Scott Thomas had a double-double with 19 points and 11 rebounds, while McElroy added 13 points. Cameron Black grabbed 11 rebounds.
Javon McCrea finished with 18 points and nine rebounds for the Bulls (8-5, 0-1).