Under former coach Bruce Pearl, the Vols had won eight of nine against the Gators before Pearl finished his career with a four-game losing streak that included a three-game sweep last season. Tennessee was especially dominant against Florida at home during that stretch, winning five of six at Thompson-Boling Arena.
"You want to protect your home court," Martin said. "Whether it's a new coach, new team, inexperienced guys or whatever you want to call it, you want to do everything in your power to try to protect your home court. The great ones find ways to win on the road."
The Vols (8-7, 1-0) protected their home court by fighting for good shots around their own basket and contesting the Gators all over the floor on the defensive end to limit them to a season-low points total.
Florida, which has lost all four of their true road games this year, came in averaging 85.4 points this season, best among SEC teams and fifth in the nation. The Volunteers held the Gators to 35.7 percent shooting while hitting 51 percent of their own attempts.
"I'm more disappointed with our defense than anything else in the game," Florida coach Billy Donovan said. "Both teams played hard, but the difference was the defense. At one point were we giving up 55 percent (shooting) in the second half. That was the issue."
Josh Richardson hit a 3-pointer 41 seconds into the second half that set the tone for the Vols the rest of the way. Cameron Tatum stole the ball from Erving Walker on the next possession and ran it down the floor for a dunk to give Tennessee a 38-31 lead.
Kenny Boynton hit a 3-pointer for the Gators at the other end. Boynton, who entered the game averaging 19.5 points, finished with 13. Erik Murphy also had 13 for Florida (12-4, 0-1) and Patric Young added 12.
Renaldo Woolridge answered with a layup for the Vols. Tatum drew a charge by Bradley Beal and after running a bit of an offensive set drove to the basket to hit a layup to make it 42-34.
The Vols expanded their lead as they hit 12 of 22 shots in the second half while the Gators hit only 8 of 27. Tennessee controlled the post in the second half and outscored Florida 32-20 in the paint.
"They were making shots," Murphy said. "They were getting a lot of easy baskets, because they were executing their offense really well. You know, we didn't guard as well as we could have. You combine those two together and they are going to score."
Smothered by defenders, Jordan McRae hit a jumper near the basket to give Tennessee a 65-49 lead with 1:57 to go, putting the game out of reach for Florida.
After starting every other game this season, Kenny Hall came off the bench to score a season-high 13 points. Jeronne Maymon and Trae Golden each added 12 points for Tennessee, while McRae finished with 10.
Tennessee had lost to its previous three ranked opponents this season by an average 5.7 points but looked listless in a 69-51 loss at Memphis on Wednesday.
The Gators held early practices all week trying to get used to Saturday's 11 a.m. Eastern tipoff time and got their customary strong performance from their starters, who are all averaging double-digit scoring this year. But Florida's reserves only managed one point, a free throw by Casey Prather.
Though Florida entered the game with the advantage in nearly every statistical category, the two teams played to a near draw in the first half, with Tennessee entering halftime with a 33-29 lead.
The Vols outshot the Gators 48.1 percent to 41.4 percent in the first half and had four more points in the paint. Thanks to a solid effort by McRae, who was relegated to the bench for the first time all season, the Tennessee reserves outscored Florida's 11-0 in the first half.
The victory gives the Vols a boost as they continue through a month that includes four more games against teams currently ranked among the top 15 in the nation. Tennessee travels to No. 15 Mississippi State on Thursday and hosts No. 2 Kentucky on Jan. 14.
"It was really good for us to get our confidence back after the loss at Memphis," Maymon said. "It's only one game, but we were just trying to start it off strong. Everybody's (SEC) record was 0-0, so we were just trying to start over like a new year."