Denzell Taylor grabbed 11 rebounds and the Monarchs (14-15, 8-6 Conference USA) outshot Marshall from the field 49 percent (25 of 51) to 37 percent (20 of 54).
Kareem Canty's back-to-back 3-pointers gave Marshall an 11-6 lead, but the Monarchs led 15-14 on a free throw by Ross. Canty scored seven straight points and Marshall led 27-23 at halftime.
Old Dominion took charge with a 9-0 run in the second-half capped by a dunk by Ross, then ripped an 8-2 run to lead 56-42. Ross put the Monarchs up 63-53 with a layup at 2:31. Canty made it a five-point game with a trey, but Bacote blunted the charge by hitting six free throws down the stretch.
Canty led Marshall (9-20, 3-11) with 24 points.