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.
“"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 said.
“"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 to have any hope of European football next year.