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.
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.
No. 17 Memphis 65, Samford 54 • At Memphis, Tenn., Adonis Thomas scored 16 points and Antonio Barton added 14 and Memphis escaped with a victory over Samford in an opening game of 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.
No. 18 UNLV 77, Jacksonville State 58 • At Las Vegas, Mike Moser scored 19 points with 10 rebounds, while Justin Hawkins added 16 points to lead the UNLV past Jacksonville State at the Global Sports Classic. Anthony Bennett had 12 points, nine rebounds, and three blocks for UNLV (2-0).
No. 23 San Diego State 60, Missouri State 44 • At 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. It was the second consecutive victory for San Diego State since the Aztecs lost the season opener against Syracuse.
• No. 4 Ohio State 69, Rhode Island 58
• No. 17 Memphis 65, Samford 54
• No. 18 UNLV 77, Jacksonville State 58
• No. 20 Notre Dame 78, BYU 68
• No. 23 San Diego State 60, Missouri State 44