A first-half Alessio Cerci goal earned the three points for the Tuscans who were being managed by Vincenzo Guerini for the first time after former coach Delio Rossi was sacked for attacking midfielder Adem Ljajic in the dug-out.
Cerci was put clean through after 35 minutes by a Ruben Olivera flick and coolly slotted home at the near post past Lecce goalkeeper Massimiliano Benassi.
Lecce trail Genoa by three points and must hope Champions League-chasing Udinese beat their relegation rivals on Sunday (1300 GMT) or they will definitely be in Serie B next term.
"I haven't taken Fiorentina to safety. This is a job done by two coaches, in particular by Rossi over the last few weeks," Guerini told reporters.
"We've avoided the humiliation of having to play for safety on the last day of the season. I have to compliment the lads, they played in terrible physical conditions. Loads of them couldn't play, and other who hadn't played in a long time did really well."
Two goals from Francesco Totti on his 500th appearance for Roma were not enough to gain a win for his hometown club as they dropped out of the race for Europe with a 2-2 home draw against Catania.
Totti, who missed a penalty in the first half, gave Roma the lead with a stunning left-foot strike seven minutes into the second period but a penalty from Francesco Lodi and another from Giovanni Marchese put the Sicilians in front.
Totti scored his 215th goal with 13 minutes left to set up a frantic finish, but despite piling on the pressure they could not find the winner and will have to hope Inter do not win Sunday's Milan derby (1845 GMT) to have any hope of European football next year.
Juventus could be crowned Serie A champions on Sunday as they take on Cagliari in Trieste (1845 GMT) in front of thousands of travelling fans.
(Reporting by Terry Daley, editing by Ed Osmond)
