Hassell finished with 15 rebounds, 12 points, three steals and three blocks for the Monarchs (22-6). Finney pulled down 13 rebounds and scored 10.
Old Dominion led 44-43 with 13:17 left to play before going on a 14-3 run, capped by a 3 from Finney, pulling ahead 58-46 with just over 9 minutes to go.
Norris Cole scored 35 points on eight 3-pointers and dished out five assists for the Vikings (23-6), who shot 33.9 percent from the floor (20 of 59). Trevon Harmon and Jeremy Montgomery each scored 12 for Cleveland State.
Kent Bazemore added 18 points, eight rebounds and four steals for the Monarchs, who have won four straight and eight of nine.
Old Dominion posted a 53-24 rebounding edge and outscored the Vikings 38-14 in the paint.