Wesley Alcegaire finished with 15 points for Bowling Green (5-2), which has won four straight following a two game losing streak.
UMBC (1-7) led by as many as seven in the first half and took a 33-29 lead into the locker room. But the Falcons stormed back in the second half and took a double digit lead on a Parker 3-point play with 4:24 left.
The Retrievers Rodney Elliot hit 1 of 2 at the line to cut Bowling Green's lead back to 67-63 with just over a minute left, but they got no closer. Ismail Ali hit a pair of free throws and Parker scored another 3-point play to put the game away.
Joe Sherburne scored 19 points for UMBC, which has lost four straight.