Leslie posted 12 of his 15 points in the first half as the Bulldogs (10-2) built a 41-20 advantage. He finished 7-of-10 from the floor and also pulled down a team-high seven rebounds in only 24 minutes of work.
Georgia's largest lead of the game came at the 15:12 mark of the second half when the Bulldogs went up 55-22 on Price's jumper.
"I thought our team played well in the first half," Georgia coach Mark Fox said. "I thought we played really well to start the second half. We got the young guys some much-needed time and experience. I thought our bench played well at times. I'm just pleased to get the win and get ready for the next one Friday."
"We played really well tonight," Thompkins said. "We had guys contribute in all aspects of the game. Everyone played a certain part in the game, and I really think we got better as a team."
Jamarco Warren recorded 24 points for the Buccaneers (6-7).
The Bulldogs have won seven in a row.
Georgia will return to action on Friday at 1 p.m. against Eastern Kentucky.