Sullivan scored eight points, including two 3-pointers, during a 15-3 run that gave the Bears (1-0) a 46-38 lead. McGonagill's 3-pointer made it 51-45 with 7:12 remaining after the Bearcats (0-2) cut the lead to three points.
Brown held Binghamton to one basket the rest of the way to win in Mike Martin's debut as Bears coach.
Freshman Cedric Kuakumensah grabbed a game-high nine rebounds for the Bears, while sophomore Rafael Maia, a Brazilian native who was ineligible for his freshman year because of an NCAA rule, scored seven points, including six in the second half.
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Shaka Smart lost five seniors and his best player. But behind a trio of talented underclassmen, the Longhorns could be building something special.
High school junior Zach Brown, a 7-footer from Miami, has rescinded his commitment to UConn, sources told ESPN.