Tennessee will next play at 4 p.m. Eastern against the winner of Texas A&M-South Carolina.
"Hard-fought game," said Head coach Holly Warlick, who got her first career SEC tourney victory. "It's survive and advance. These young ladies found a way to win."
SEC Co-Player of the Year Meighan Simmons led the way with 20 points. Taber Spani notched 13 points, Cierra Burdick had 14, Kamiko Williams added 12, and Bashaara Graves and Ariel Massengale had 10 each.
Sydney Moss led the way for the Gators with 22 points, while Jaterra Bonds added 18.
"We're obviously very disappointed," Florida coach Amanda Butler said. "We didn't come here to play close or make is respectable, with any other expectation except to win."
Tennessee had its own defensive lapses that will need to be corrected, but the Lady Vols can score. They shot 48.2 percent for the game and 82.1 percent from the line.
"I think on the offensive end, we're just talented," Burdick said. "We've got a bunch of people that can score the basketball."