Mosely was 10 of 16 from the floor with four 3-pointers. Nathan Dieudonne scored 13 points and Nick Havener added 12 for the Terriers (3-3). Kyle Foreman chipped in seven points with six assists and three steals.
The Terriers had an 8-point lead at halftime. Rodriquez scored six straight points to pull the Bearcats to 48-44. Havener made a jumper and Foreman made two free throws to stretch BU's lead to 62-49 midway through the second half.
Everson Davis scored four points and Rodriguez a layup to cut the Terriers' lead to 69-63 with 1:26 to play. BU made 6 of 8 from the line to seal it.