Alessio Cerci scored the only goal of the game 10 minutes before halftime. Lecce goalkeeper Massimiliano Benassi almost equalized in injury time but his strike hit his own teammate.
In the late game, Francesco Totti scored twice and had a penalty saved as Roma drew 2-2 with Catania in the veteran striker's 500th Serie A match.
Lecce is three points off Genoa, which plays Udinese on Sunday. Lecce still has a slight chance of avoiding the drop if Genoa loses its last two games.
Lecce must win its final match at Chievo Verona next weekend to survive on goal difference, as it has a level head-to-head record with Genoa. Both games between the sides finished in a draw.
Guerini took charge of Fiorentina after coach Delio Rossi was fired for slapping a player.
A draw at title-seeking Juventus midweek reignited Lecce's hopes of survival and Serse Cosmi's team had the best of the opening chances.
However, Fiorentina came into the game after half an hour. Mattia Cassani should have scored when Ruben Olivera backheeled the ball into his path but Benassi did well to save his low shot.
Fiorentina was in front minutes later as Olivera touched on Felipe's long throw and Cerci beat the offside trap to put an unstoppable shot past Benassi.
Cassani could have doubled Fiorentina's lead soon after—following a swift one-two with Riccardo Montolivo—but his shot hit the outside of the post.
Lecce came close to leveling just before halftime but Valeri Bojinov blazed over the bar.
The home side went even closer shortly after the break when Andrea Esposito tried to lob rushing Fiorentina goalkeeper Artur Boruc but crashed his effort off the crossbar.
Benassi went close to snatching a vital point when he came up for a corner deep into injury time when his volley hit team mate Guillermo Giacomazzi.
In Rome, Totti should have got his side off to a brilliant start when Juan Pablo Carrizo was adjudged to have brought down Roma striker Fabio Borini.
However, the Catania goalkeeper atoned for his error by parrying Totti's spot kick and the Roma captain blazed the rebound over the bar.
Totti did get on the scoresheet seven minutes into the second half after he was picked out by Fernando Gago. Totti did well to carve out some space for himself before curling a left-footed shot in from just outside the area.
Catania was level shortly afterwards when Gabriel Heinze tripped Pablo Barrientos in the area and Francesco Lodi converted the resulting penalty, sending Roma goalkeeper Bogdan Lobont the wrong way.
The visiting side took the lead 10 minutes later. Lodi turned provider to send a free kick near the corner flag out for the onrushing Giovanni Marchese to volley home.
However, Roma leveled when Totti slotted home Miralem Pjanic's cross.
Roma was somewhat unfortunate not to be granted a penalty in the dying minutes when Nicola Legrottaglie appeared to bundle over Bojan Krkic in the area.