Ohio State (13-4, 3-2) was playing for the first time since handing Michigan its only loss last Sunday.
The Buckeyes' second-leading scorer against the Spartans was Lenzelle Smith Jr., who had six points on 2-of-7 shooting. Aaron Craft, who was 2 of 8 from the field, was one of three Buckeyes with five points.
''You'd like to have everyone in double figures, but (Thomas) was smooth and efficient and it was a tremendous effort by him,'' Matta said.
The Spartans were ahead by 11 points early in the first half and had a 46-39 lead midway through the second half.
Michigan State kept the lead until Thomas made a 3-pointer - his sixth of the game, two more than he's ever had - to tie it at 50 with just less than 3 minutes left.
Payne had a three-point play on the ensuing possession. Then MSU went right back to Payne on its next trip. Payne was swiped by Craft as he began to make a move against Thomas.
On the next trip, Craft then stole the ball from Appling and made a pass to Thomas, who was fouled and made two free throws to tie it again with 57.9 seconds left.
Appling went right back at Craft, beating him to the lane off the dribble to set up his go-ahead layup with 41.5 seconds to play.
After Ohio State missed a 3-pointer, Dawson grabbed the defensive rebound, flipped it out to Appling, who ran out for a dunk with 17 seconds left to put Michigan State ahead by four points.
Smith made a 3-pointer on the ensuing possession to pull Ohio State within a point, but the Buckeyes needed to make one more to force overtime.
And, they didn't give Thomas an opportunity to make it.
''I did think he was going to get the ball,'' Payne said. ''I was trailing him, but the other guy fired it up.''
Michigan State made enough plays at both ends of the court to beat the Buckeyes at home for a change. Ohio State has won four games at the Breslin Center since 2005-06 while the rest of the conference has combined for six wins in East Lansing.
''You've got what I would consider - I don't want to step out of bounds - two of the top college basketball programs going head to head,'' Matta said. ''I've brought some great teams in here.''