Llorente double leaves Napoli third
Spaniard Llorente, who scored in Napoli's midweek 2-0 win over Champions League holders Liverpool, grabbed the opener on 28 minutes at the Stadio Via del Mare. He added a late fourth for Napoli eight minutes from time.
"It was a game that could have been a trap after the high of Liverpool, but the many changes helped us," said Napoli coach Carlo Ancelotti.
Arkadiusz Milik started up front alongside Llorente with David Ospina back in goal. And Polish striker Milik's assist contributed to Llorente's opener.
"In the first half we were a bit lazy, but otherwise the performance was good for the whole 90 minutes," continued Ancelotti.
"From a mental point of view the team was excellent, we managed the game and brought it home safely."
Lorenzo Insigne scored Napoli's second goal from the spot five minutes before the break, on his second attempt after Lecce's goalkeeper left his line prematurely before he saved the first.
Fabian Ruiz scored Napoli's third on 52 minutes before Marco Mancosu pulled a goal back for Lecce after an hour - the eighth conceded by Napoli in four league matches.
Ancelotti's side sit third, three points behind leaders Inter Milan, who are on maximum points after four games, after their thrilling 2-0 Milan derby win on Saturday.
Champions Juventus won 2-1 at home against Verona and are second with 10 points from four games.
"Juve still look to be under construction," warned Ancelotti.
"Knowing (coach Maurizio) Sarri and his teams, I think he is still fine-tuning things. Inter are already up and running, Juventus will get there in the coming matches."
In Bologna, Dzeko's late winner sealed a 2-1 win for 10-man Roma, who are fourth a point behind Napoli.
The Romans were hit by Gianluca Mancini's sending off on 85 minutes, but Dzeko picked up a Lorenzo Pellegrini pass to finish off four minutes into injury time.
Aleksandar Kolarov had opened the scoring just after the break before Nicola Sansone hauled Bologna level from the spot on 54 minutes.
Sampdoria moved off the bottom of the table earning their first points thanks to Manolo Gabbiadini's goal against Torino, who fell to their second consecutive defeat.