Alessio Cerci put the Viola in front in the 35th minute and the visitors' Mattia Cassani almost doubled the lead before the interval when his effort hit the post.
Lecce, without suspended pair Luis Muriel and Juan Cuadrado, were denied by the crossbar early in the second half and fell to a costly defeat.
While the Tuscans have climbed nine points clear of the drop zone, third-bottom Lecce are one place and still three points behind Genoa.
If Genoa get a point on Sunday at Udinese, Lecce will be relegated with one round of games still to play.
Fiorentina went into the game under a dark cloud with club coach Delio Rossi having been sacked for his attack on midfielder Adem Ljajic during Wednesday's 2-2 draw with Novara.
Ljajic was left out of the squad for disciplinary reasons and the Viola were led by team manager Vincenzo Guerini, who coached his first Serie A game in 14 years.
The visitors could have gone in front in the 25th minute but Lecce goalkeeper Massimiliano Benassi made a one-handed save to clear Riccardo Montolivo's drive from 30 yards.
Shortly after the half-hour mark, Benassi was called again to make a vital clearance from Cassani's goal-bound effort.
Benassi could do little to deny Fiorentina the lead when Ruben Olivera fed Cerci in the box and his left-footed strike beat the keeper.
Cassani then saw his right-footed shot from the edge of the area hit the far post.
Lecce pressed forward more aggressively after the re-start and almost equalised in the 51st minute.
Andrea Esposito's close-range header from Andrea Bertolacci's cross beat Fiorentina goalkeeper Artur Boruc but struck the crossbar.
With 15 minutes remaining, Lecce's Davide Brivio struck the ball just wide of the far post from outside the area.
The hosts continued to attack but could not find a way through the Fiorentina defence.
Lecce end the campaign at Chievo while Fiorentina host Cagliari next.