The Rams (12-16, 3-10 Atlantic 10) shot 50 percent from the floor, with Munford shooting 10 of 19 and Matthews finishing 8 of 16. Gilvydas Biruta contributed 11 points.
The Bonnies led 43-33 at halftime, but Rhode Island stormed into the lead in the second half with a 12-2 run fueled by 10 points from Munford. St. Bonaventure pushed back into a five-point lead, but Matthews hit a layup, 3-pointer and two free throws to pull ahead by four with 2:25 remaining.
A three-point play by Biruta and a 10-for-10 finish from the line put the game out of reach.