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.
Diego Maradona enjoys a wild night in Naples after he attended a ceremony and received honorary citizenship from the Italian city.
Two goals each from Stephan El Shaarawy and Mohamed Salah keep Roma's Serie A title hopes alive as they twice came from behind to win 5-3 at Chievo Verona, while Napoli also stays in the running with a 4-1 home win over Fiorentina.
Gonzalo Higuain scored twice on his old Napoli hunting ground to send Juventus into the Italian Cup final despite a 3-2 defeat to their bitter rivals on Wednesday.
Serie A leaders Juventus withstood prolonged pressure as they held out for a tense 1-1 draw at third-placed Napoli in an absorbing match on Sunday.
Napoli were left fuming after Juventus were awarded two penalties early in the second half on their way to a 3-1 win in the first leg of their Italian Cup semi-final on Tuesday.
Napoli's remote hopes of overhauling Serie A leaders Juventus were dealt a possibly fatal blow when they lost 2-0 at home to Atalanta on Saturday and the Turin side ploughed on by beating Empoli by the same score.
Bayern Munich routed Arsenal 5-1 in their Champions League last 16 first leg clash on Wednesday thanks to a blistering spell of three goals in 10 second-half minutes.
Napoli scored in the fifth minute of stoppage time to snatch a 2-1 win over Sampdoria who had a player controversially sent off as Serie A resumed with a bang on Saturday.
Napoli substitute Manolo Gabbiadini converted a penalty with the last kick of the game to salvage a 3-3 draw at Fiorentina who were inspired by a superb display from Federico Bernardeschi.
Dries Mertens put four goals past England's Joe Hart as rampant Napoli completed a memorable 5-3 win over Torino to move up to third place in Serie A Sunday.
