Steven Swavely scored a first period goal to give the Black Bears a 1-0 lead.
The game was still 1-0 when the third period started.
The Black Bears scored three goals in the final period including Mike Cornell and Beattie scoring 19 seconds apart.
Devin Shore recorded two assists for the Black Bears. Martin Ouellette finished with 31 saves on 34 shots.
Maine (11-17-7) clinched a berth in the Hockey East tournament thanks to their win and Massachusetts losing to Merrimack.
The Black Bears will finish the regular season on Saturday with another contest at New Hampshire. The game can be seen live at 4 p.m. on NESN.
The hockey east tournament will start on March 14th.