The Bearcats (6-25, 5-11), who notched their highest conference win total since the 2009-10 season, will be the No. 6 seed in the America East Conference tournament and will play at No. 3 Stony Brook on Wednesday. With Maine's loss to New Hampshire earlier Saturday, UMBC (4-25, 2-14) ended up with the No. 7 seed and will play at No. 2 Vermont on Wednesday.
Grace hit one of his five 3-pointers to get UMBC within four, 69-65, with 2:09 left but Beck responded with a 3-pointer and the Bearcats added four free throws in the final minute.
Binghamton took 31-24 lead at halftime behind 11 points from Beck.