Richard Ross added 14 points and Ambrose Mosley 12 for the Monarchs (20-6, 9-5 Conference USA), who had lost their previous five conference road games. The career-high rebounds gave Freeman his first double-double and Old Dominion a 30-23 advantage on the boards.
Max Guercy had 20 points to lead Rice (10-16, 7-7), which shot 42 percent and had 16 turnovers.
Old Dominion scored the first nine points of the game but led Rice get within three before scoring eight straight, including two 3-pointers by Freeman, to lead 30-20 at the half.
Denzell Taylor and Freeman scored the first two baskets of the second half and Old Dominion maintained a double-figure lead throughout the second half until J.T. Trauber's 3-pointer with 19 seconds left ended the scoring.