The win improved league-leading Morgan State to 16-9 overall and 10-2 in the Mid-Eastern Athletic Conference. The Bears have won nine of their past 10 games.
Bethune-Cookman, which has lost four of its past six, fell to 10-16 overall and 4-8 in the conference.
John Holmes led Bethune-Cookman with 17 points, with Dominique Whatley and Dewayne Pettus each adding 13.
Two other Bears were in double figures, with Boubacar Coly and Jamar Smith each scoring 10. Coly also had a game-high 14 rebounds, as the taller Bears dominated the glass 31-21.
Green, who went 11-for-14 from the foul line, led the way as Morgan State surged to a 13-point lead (43-30) with 10:06 to play. Holmes worked mostly inside in helping the Wildcats close the margin to seven (45-38) with 6:31 to play. But Bethune-Cookman got no closer as the Bears gradually pulled away.
Coppin State 69, Florida A&M; 68 -- Antwan Harrison's tip-in with six-seconds left lifted the visiting Eagles over the Rattlers. Coppin State (9-19, 4-8 Mid-Eastern Athletic Conference) trailed by one with less than 30 seconds left, but they rebounded Akini Akini's air ball and pushed it the other way. Julian Conyers' jumper from the elbow rimmed out, but Harrison tipped in the rebound.
Loyola 63, Siena 56, OT -- Loyola held the Saints (9-16, 5-10 Metro Atlantic Athletic Conference) to just four points in overtime, and seniors Tynisha Davis, Vika Sholokhova and Meghan Wood led the visiting Greyhounds (12-13, 7-8) to a victory.
Bowie State 85, Allen 46 -- The host Lady Bulldogs (19-5) led from the start and routed the Yellow Jackets (0-25) in a nonconference game. Bowie State senior Allyson Swailes scored a game-high 14 points.