Lenzelle Smith Jr. added 15 points, Aaron Craft had 13 points and four assists for the Buckeyes (2-0) who struggled with the Rams (0-3) well into the second half.
Xavier Munford had 16 points to lead Rhode Island, which had four players in double figures and trailed by just four at halftime.
The Rams were down just six when Craft hit a 3-point shot that bounced around the rim and in with 6:45 left and then stole the ball on the other end of the court.
That led to a technical foul on Rhode Island coach Dan Hurley.
Thomas hit both free throws and the five-point swing gave Ohio State a 55-44 edge, its first double-digit lead of the game, and the Buckeyes held on from there.
Rhode Island hit eight of its 17 shots from 3-point range to stay in the game, but was outrebounded by 10.
NO. 17 MEMPHIS 65, SAMFORD 54
In Memphis, Tenn., Adonis Thomas scored 16 points and Antonio Barton added 14 points and Memphis escaped with a victory over Samford at the Battle 4 Atlantis Tournament.
Joe Jackson added 13 points, four assists and three steals for Memphis (2-0), which converted all eight of its free throws in the final minute to preserve the victory.
NO. 20 NOTRE DAME 78, BRIGHAM YOUNG 68
In New York, Jack Cooley had 19 points and 13 rebounds to lead Notre Dame to a victory over Brigham Young in the third-place game of the Coaches vs. Cancer Classic.
Jerian Grant had 19 points –17 in the second half – and Eric Atkins added 16, including the 3-pointer that gave the Fighting Irish a cushion after the Cougars had pulled within 63-61 with 4:28 to play.
Cooley was 7 of 12 from the field as the Fighting Irish shot 52.1 percent from the field (25 of 28) and were 22 of 28 from the free throw line overall in the victory.
NO. 23 SAN DIEGO STATE 60, MISSOURI STATE 44
In Springfield, Mo., Jamaal Franklin scored 15 of his 22 points in the first half to put San Diego State up early, and James Rahon hit a key 3-pointer late in a win over Missouri State.
The Aztecs led 39-30 midway through the second half before the Bears rallied. Missouri State (1-1) pulled within 41-37 on Anthony Downing’s basket with 7:13 left.
But the Aztecs pulled away thanks to 3-pointers on consecutive possessions from Rahon and Chase Tapley.
It was the second consecutive victory for San Diego State since the Aztecs lost the season opener against Syracuse.