Jared Terrell added 13 points for Rhode Island (4-1), which will play in Sunday's fifth-place game. Matthews had 20 points in the Rams' 76-60 loss Thursday to Kansas.
Santa Clara (2-4) got 14 points from Brandon Clark and 10 from Matt Hubbard. The Broncos will conclude the tournament by playing in Sunday's seventh-place game.
Matthews had 11 points as Rhode Island went up 35-27 at halftime. His 3-pointer put the Rams up 43-27 6 minutes into the second half.
Santa Clara forward Yannick Atanga hasn't played at the classic due to a knee injury which coach Kerry Keating said could sideline the senior for the rest of the season.
Rhode Island shot 53 percent (25 of 47) from the floor and was 8 of 18 (44 percent) on 3-pointers.