Frank Anguissa and Amir Rrahmani scored Napoli's goals in an eight-minute spell in the first half before Andrea Pinamonti cut the deficit early in the second period.
Fiorentina earlier remained on Napoli's heels after their 1-0 home win over Cagliari in their first league match since midfielder Edoardo Bove's sudden collapse last weekend.
Lazio will face either Inter Milan or Udinese in the quarter-finals.
Napoli coach Antonio Conte criticised the Video Assistant Referee (VAR) for not intervening to reverse a penalty that Inter Milan's Hakan Calhanoglu eventually missed in their 1-1 draw on Sunday.
Antonio Conte's resurgent side wrapped the match up inside the first half, courtesy of an early Romelu Lukaku goal and a sensational strike by Khvicha Kvaratskhelia.
Victor Osimhen has been sidelined by Napoli after the team he fired to Serie A glory just a over year ago left him both off their squad list for the 2024/25 campaign and potentially in season-long limbo.
Belgium striker Lukaku completed a permanent move to Napoli from Chelsea on Thursday, ending a long period of limbo with the Blues.
The futures of Napoli striker Victor Osimhen and England international Ivan Toney are set to dominate the final day of the European transfer window on Friday as Chelsea continue their frenzied pursuit of new signings.
Napoli manager Antonio Conte apologised to the club's fans after his side were humbled 3-0 at Hellas Verona in Serie A on Sunday and said he took responsibility for the loss.
Dries Mertens scored four goals, including a nine-minute first-half hat-trick, as Napoli forgot their scoring problems with a 5-3 win over Torino in Serie A on Sunday.
Dries Mertens scored a hattrick to lead revitalised Napoli to a 5-0 rout at leaky Cagliari in Serie A on Sunday.
Inter Milan scored three early goals before surviving a second-half fightback to beat 10-man Fiorentina 4-2 and give new coach Stefano Pioli his first win on Monday.
Napoli striker Arkadiusz Milik could be out for several months after suffering a knee injury in Poland's World Cup qualifier win against Denmark.
Champions Juventus returned to the top of Serie A with a 4-0 home rout of Cagliari on Wednesday, while former leaders Napoli dropped to second after being held to a goalless draw at Genoa.
Juventus manager Massimiliano Allegri says he can't wait to start working with his 90 million euro man Gonzalo Higuain but warns the striker.
Gonzalo Higuain "betrayed" Napoli by joining rivals Juventus, claims club owner Aurelio De Laurentiis despite pocketing 90m euros.
Gonzalo Higuain completes a sensational move to Juventus after the Italian champions agree to pay a 90 million euros ($98.8m) fee, the third highest in history, to wrest the Argentine striker from Napoli .
Preliminary reports emerging from Italy are confirming that Napoli striker Gonzalo Higuain has signed for Juventus after a drawn-out transfer saga.
Juventus are set to smash Italy's transfer record by snatching striker Gonzalo Higuain from Napoli after triggering his release clause of 94.7 million euros ($104 million).
