Brown led 30-29 at the break, but Edwards' three-point play early in the second half helped spark a 19-7 Maine run over a 7 1/2 minute span for a lead that would stick.
Maine outscored Brown 42-28 in the second half to clinch the comeback.
Mike Allison had a game-high 10 rebounds for Maine, which outrebounded Brown 42-30. Singleton hit 3 of 4 from beyond the arc, as Maine outshot Brown 50 percent (6 of 12) to 23.1 percent (3 of 13) from long range.
Matt Sullivan scored 15 points to lead Brown (5-8), which has lost four of its last five.