The game matched teams that won their conferences a year ago but were trying to replace three lost starters.
By scoring 13 of 18 points at the end of the half, the Buckeyes took a 35-32 lead.
They scored the first five points of the half for an eight-point edge and never let the Gators cut into the lead.
Still, Sullinger picked up his third foul with 13:58 left and soon after headed to the bench. With Evan Ravenel filling in and Buford and Craft setting the pace on offense, the Buckeyes didn't blink at the loss of their preseason All-American.
Ravenel had two baskets in a 6-1 run for a 50-38 lead. Buford scored six in a row for Ohio State to swell the lead to 59-44.
A rested Sullinger then returned to the lineup.
The foul line helped the Buckeyes maintain their advantage the rest of the way. Florida was just 13 of 21.
The Gators set the tempo early on three 3s by Murphy, building a 14-6 lead.
Ohio State came within a shot of tying it on several occasions before finally catching Florida on Craft's steal on one end and a twisting, spinning layup through traffic at the 3:24 mark.
That was part of a 13-5 run to end the half. The key basket was Sullinger's fadeaway 15-foot jumper with a second left on the shot clock that put the Buckeyes up 33-31. Ravenel, a transfer from Boston College who is considered mostly a defensive replacement, hit a short jumper in the final minute as the Buckeyes took a 35-32 lead.
After hitting just 2 of 7 shots from the field to start, the Buckeyes hit 10 of their last 19.
Murphy had nine points, all from outside, Boynton and Beal seven each and Rosario five off the bench for the Gators, who had nine turnovers at the break.
Ohio State has won eight of the 12 meetings, but the Gators captured the big one. They beat the Buckeyes 84-75 to clinch their second straight national championship on April 2, 2007.
The Buckeyes went to Gainesville, Fla., last year and routed the Gators 93-75.
It was Ohio State's 24th consecutive victory at home. The Buckeyes are now 69-2 against non-conference opponents in Columbus under coach Thad Matta.