The Terriers won for the sixth straight game and tied Vermont for the top spot in the conference at 7-2. UMBC fell to 9-13 overall and 3-7 in the league.
Terrier freshman forward Jake O'Brien led all scorers with 25 points and was BU's America East Player of the Game.
The Retrievers opened the second half by hitting eight of their first 11 shots, but could not close ground as O'Brien scored 13 points in the first eight minutes of the half.
Wolff made one of two free throws, and BU wing John Holland hit a three-pointer on the ensuing possession. After Spadafora hit a pair of free throws, Holland buried another long three to give the Terriers a secure 73-63 advantage with 2:37 remaining.