The RedHawks (7-9, 2-0) led 65-63 with 1:15 left before two free throws from Mitchell Watt tied the score at 65 with 53 seconds remaining.
Nick Winbush hit a 3-pointer with 28 seconds on the clock and Quinten Rollins knocked down two free throws with 13 seconds to go to help Miami seal the victory.
Antonio Ballard and Winbush scored 15 points apiece for the RedHawks, who shot 53.3 percent from the floor (24 of 45).
The Bulls (8-6, 0-2) were led by Javon McCrea's career-high 26 points, but his layup with 1:59 left was Buffalo's final field goal of the game.
The RedHawks led 28-16 with 8:18 left in the opening half, but were outscored 14-3 over the next 5:02 and held a 38-37 advantage at halftime.