Binghamton took a 14-11 when Jordan Reed put in a layup with 12:09 remaining in the first half.
The Black Bears went on a 16-2 run to take a 27-16 lead, and cruised from that point in their conference opener.
Kilian Cato led the Black Bears with 17 points.
Dimitry Coronel recorded 14 points, 10 rebounds, and three assists. Zarko Valjarevic added 14 points and three steals.
Troy Reid-Knight came off the bench to score 10 points in 11 minutes.
Maine (3-10/1-0) will travel to Hartford on Thursday.