For much of the second half Matthews single-handedly outscored Detroit 18-17. Rhode Island (7-3) is 5-0 at home.
The first half was quite different as Juwan Howard scored 13 for Detroit (6-6), and the Titans bench outscored Rhode Island's 23-12 en route to a 36-34 lead at the half.
But Howard was tightly guarded after halftime, taking seven shots - and not making one till 3:53 remained and Detroit down by 17. He finished with 17 points, his other four starters adding only four more.
Rhode Island opened the second half 19-4, taking control of the game. Aside from shutting down Howard, the Rams sank 26 of 34 from the line, forced 18 turnovers and blocked seven shots, Hassan Martin with four.