Alessio Cerci scored the only goal of the game as Fiorentina won their first game since Delio Rossi was sacked as coach of the club.
The away side had the better of the opening exchanges and created two goalscoring opportunities.
However, Ruben Olivera and Riccardo Montolivo were unable to get their efforts from inside the area on target.
Fiorentina continued to dominate as the half progressed an eventually broke the deadlock in the 35th minute. Olivera threaded a pass through to Cerci, who sent a left footed shot into the bottom left hand corner of the net.
Lecce responded positively after the break and went close to restoring parity in the 51st minute. Andrea Bertolacci sent over a cross for Andrea Esposito, who sent a headed effort against the bar.
David Di Michele had two chances for Lecce in the closing stages, but the veteran failed to find the back of the net on both occasions.
The loss has left Lecce in the Serie A relegation zone.
