The Bonnies (11-7, 4-2 A-10), who trailed 40-30 at halftime, opened the second half on a 19-6 run to take a 49-46 lead with 9:42 left to play. Rhode Island fought back to tie the game 61-all with 1:10 left but neither team could score before the end of regulation.
St. Bonaventure controlled overtime, outscoring the Rams 11-5 and forcing three turnovers. All five of Rhode Island's overtime points came on free throws as the Rams were 0 for 6 from the field during the period.
Rhode Island (3-18, 0-6) shot 39 percent (23 of 59) from the field and were outrebounded 46-35.
Jonathan Holton led the Rams with 16 points and 11 rebounds.