Cincinnati tied the game with 13.5 seconds remaining after being down by five with 1:25 left in the game.
After UConn took a timeout, Boatright took the inbounds pass, drove down the court and hit the game-winning shot.
Boatright finishedwith 18 points, four assists and three rebounds. Rodney Purvis scored 18 points for UConn.
UConn, the defending national champions, will play Tulsa on Saturday at 5 p.m. ET.