Thompson finished with 19 points for Ohio State (22-6, 9-6 Big Ten), which trailed 28-18 at the half before rallying to notch a sixth win in seven games.
Lenzelle Smith Jr. added 13 points and Shannon Scott netted 10.
Andre Hollins paced the Golden Gophers (17-11, 6-9) with 13 points. Deandre Mathieu scored 12 for Minnesota.
Pistorius testifies he didn't consciously pull trigger when he shot girlfriend
Pregnant Mila Kunis wins 'Best Villain' at MTV Movie Awards