Henry Ellenson scored 21 points and grabbed 16 rebounds to lead Marquette.
Bradds scored six points during a 13-4 run to break a 63-all tie and gave the Bruins a 76-67 lead. Ellenson and Duane Wilson each scored 5 points, and Sandy Cohen III made a 3-pointer and the Golden Eagles regained the lead, 80-79 with 1:23 remaining.
Wilson missed a 3-point attempt, and Bradds pulled in the carom with 45 seconds left. Austin Luke made 3 of 4 free throws and Bradshaw made one to seal it.