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.
With the Suns drafting Tyler Ulis, they now have Five guards on their roster who attended Kentucky.
NBA fans will be looking forward to their newest players making plays like this next season.
Tim Legler and Brad Daugherty analyze Ben Simmons and Brandon Ingram, the top two picks in the NBA draft, and agree that Simmons will have a more immediate impact.