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.
Italy's highest court cleared the late Agentine soccer legend Diego Maradona of tax evasion charges, ending a 30-year-long legal battle between the ex-Napoli striker and revenue authorities.
Defending Serie A champions Napoli saw their non-winning league ways continue Friday with a goalless draw against mid-table Monza.
Yann Bissek's first goal in Italy just before half-time at the San Siro and a late finish from Nicolo Barella were enough for Inter to bounce back from cup defeat to Bologna midweek and keep closest challengers Juventus at bay.
Victor Osimhen has signed a contract extension with Napoli until 2026, the Serie A champions announced on Saturday.
The Italian champions qualified second in Group C behind Real Madrid thanks to Serder Saatci's clumsy own goal and Victor Osimhen's first strike since early October, both which came in the first half.
Osimhen, who led Napoli to win the Italian League title last season, beat Paris Saint-Germain's Morocco right-back, Achraf Hakimi and Liverpool's Egypt winger, Mohamed Salah, to win the top award.
Real Madrid romped to a 4-2 win over Napoli on Wednesday to qualify in first place from their Champions League group.
Mazzarri's team are still seven points behind leaders Inter Milan who travel to Turin on Sunday for the weekend's big match at second-placed Juventus
Inter Milan and Juventus face off on Sunday in a clash between Serie A's two title favourites and historic rivals, as Walter Mazzarri begins his second reign at troubled Napoli.
Napoli continued their struggles on home turf with Sunday's shock 1-0 defeat to Empoli which left the Serie A champions already well off the pace in this season's title race.
