The Tigers (17-4, 7-3 Southeastern Conference) trailed by eight points with 4:02 remaining, but closed the game on a 15-4 run.
Jaime Lloreda had 19 points and nine rebounds for LSU, ending his streak of double-doubles at five. He struggled after rolling his right ankle early in the first half and again midway through the second, and missed two free throws with 20 seconds left.
Anthony Roberson hit a 3-pointer with 5.4 seconds to go to bring Florida (14-7, 5-5) within 72-70. After Lloreda made one free throw a second later, Christian Drejer's 30-foot heave at the buzzer fell short.
Florida, which missed six of its last seven shots, lost for the third time in four games.
Matt Walsh scored 24 points to lead Florida, while Roberson had 18 points, six rebounds and five assists.
LSU trailed 66-58 after Walsh's season-high sixth 3-pointer, but scored the next 10 points. Mitchell's fast break layup with 1:56 remaining tied the game, and his free throws 24 seconds later gave the Tigers their first lead since 29-28.
Mitchell was 6-of-9 from the field and 2-of-3 from the line.
He hit three 3-pointers and a jumper for 11 straight points as LSU took an 18-12 lead. Mitchell finished 4-of-6 from beyond the arc, making him 13-for-19 over his last three games.
The Tigers briefly pushed the lead to nine points, but Florida steadied itself until Roberson could take control. His 3-pointer and fast break layup on consecutive possessions sparked a 12-0 run, and the Gators led 33-32 at halftime. Roberson also had three rebounds and a steal, all leading to Florida baskets.
Walsh hit a 3-pointer on the second half's first possession, then followed with a bank shot off an inbounds pass and another 3. That put the Gators up 43-34 and capped a 22-5 burst.