Rhode Island consistently got inside and drew the fouls, making 27 of 33 free throws. Saint Louis made 26 of 34 free-throw attempts.
Hassan Martin was 7 of 9 from the floor for 18 for the Rams (17-6, 9-3).
Rhode Island started the second half with a 13-6 run and led 67-50 with 9:06 left. Austin Gillmann drove for a layup to start an 8-0 run for the Billikens to close to 68-58, but could get no closer.
Miles Reynolds had 21 points for Saint Louis (10-15, 2-10).
Rhode Island, which has won six of its last seven games, remained tied atop the conference with Dayton and Virginia Commonwealth, which both won Saturday. UMass is a half-game back going into its game against Duquesne.