Miami (10-15, 6-8 Mid-American Conference) scored 15 straight early in the game, including seven from Moore, and led 35-25 at the break.
Bowling Green (11-16, 5-9) chipped away the entire second half, cutting its deficit to one at 53-52 on Richaun Holmes' jumper with 1:47 left. But Geovonie McKnight and Moore both made 1 of 2 free throws inside 29 seconds and Bowling Green missed its last two shots to fall short at the end.
Miami was just 4 of 14 from beyond the arc, but Bowling Green was worse - just 2 of 13.
Spencer Parker led Bowling Green with 18 points on 8 of 11 shooting. Cameron Black gathered 10 rebounds to go with eight points.