Sheldon McClellan added 20 points and five rebounds. It is Miami's first tournament win since it went to the Sweet 16 in 2013. The Hurricanes advance to play the winner of Arizona and Wichita State in the second round of the South Region on Saturday.
Miami (26-7) kept the Bulls at bay for most of the second half, leading by as many as 12. The Bulls (20-15) finally got some traction, closing within 72-68 on a jumper by Lamonte Bearden with less than two minutes to play. But Miami hit enough free throws down the stretch to put the game away.
Nick Perkins had 20 points and six rebounds to lead Buffalo. Bearden added 19 points. Miami trailed by 9 points about midway through the first half, before surging to take a 2-point halftime lead.
Buffalo tried to sag in on Miami's big men in the second half, but were bitten several times when the Hurricanes were able to get the ball out to the perimeter for open 3s. Buffalo coach Nate Oats promised his team would come out attacking, and it did, connecting on four of their first five from beyond the arc to take an early 12-6 lead.
But Miami pecked away the rest of the have and took a 35-33 lead into the locker room after Bearden's layup at the buzzer was waved off.