The win snapped the Panthers' five-game losing streak, their longest since the 2013-14 season.
Florida International (5-7) led 34-27 at the half and used a 14-2 run that was capped by a 3-point play by Adrian Diaz to open up a 53-37 lead with eight minutes to play. Binghamton trailed by double figures the rest of the way. McGill's layup with 4:35 left gave FIU its biggest lead, 63-44.
Daviyon Draper scored 13 points and grabbed 10 rebounds for Florida International.
Willie Rodriguez and Everson Davis each scored 11 points for Binghamton (2-9).
Binghamton committed a single-game, school-record three turnovers but shot just 26.3 percent from the field.
Florida International made 27 of 52 (52 percent) field goals attempts and outrebounded the Bearcats 45-26.