Walker also finished with 19 points, 14 in the second half. Vernon Macklin added 13 points and 10 rebounds for Florida, which has won three in a row.
The Gators used a 27-6 run — highlighted by four 3-pointers and a bunch of points in the paint — to turn a close game into a lopsided affair.
The victory snapped Tennessee's six-game winning streak in the series and gave Florida's NCAA tournament resume a much-needed boost.
The Gators (20-8, 9-4 Southeastern Conference) won for the fourth time in the last 15 meetings and jumped the Volunteers (20-7, 8-5) in the Eastern Division. More importantly, Florida probably secured a spot in the NCAA field for the first time in three years.
Scotty Hopson led Tennessee with 20 points. Wayne Chism, who torched Florida in the first meeting, had seven points and one rebound before fouling out with 4:02 remaining. Chism dropped to his knees near the bench, clearly in pain from a hard fall in the second half.
There was little he could have done to stop this onslaught.
Florida came alive in the second half, with Macklin, Parsons and Walker doing most of the damage.
Macklin dominated the Vols inside, and Parsons was active on the break and on the offensive glass. Walker got most of his from behind the arc.
The 5-foot-8 point guard hit three 3s in a 2-minute span, the Parsons made another that put Florida up 70-50 with 3:04 to play.
The huge run sent SEC commissioner Mike Slive, Connecticut athletic director Jeff Hathaway and most of the sellout crowd to the exits. Hathaway is a member of the NCAA selection committee, and Florida picked a good time to play its most complete game since beating Michigan State and Florida State in November.
Florida, whose RPI is 54 and whose strength of schedule is 71, improved to 3-6 against teams in the RPI's top 50.
The Gators scored the final seven points of the first half to tie the game at 37. All of them came in the paint — no surprise since Tennessee seemed content to play guards Walker and Kenny Boynton outside the 3-point line, leaving plenty of room in the paint.
Florida scored 26 points in the lane in the first half.
The Gators needed every one of them to stick with the Vols, who hit six 3-pointers in the opening 20 minutes and had just four turnovers.
Florida, meanwhile, missed eight of nine from behind the arc. The lone 3-pointer? Boynton banked one in late in the first half.
Coach Billy Donovan kept calling for his team to pound the paint, feeding Alex Tyus and Macklin every time down the court. Not only did it work, but it helped get Chism and Brian Williams in foul trouble. Chism picked up his second with 16:21 remaining, and Williams got called for his third with 2:39 to play.
Chism picked up two more early in the second half and went to the bench with 16:01 remaining. The Gators took advantage, pounding the ball inside.