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.
New Chelsea signing Kalidou Koulibaly may not yet have had a chance to introduce the Premier League audience to his football skills but he has already gained fans' respect after he called former captain John Terry to ask for his shirt number.
Kalidou Koulibaly has said goodbye to Napoli as he nears a move to Chelsea, saying: “you have been everything for me”.
Napoli defender Kalidou Koulibaly scored an injury-time own goal to hand Juventus a 4-3 Serie A victory in Turin on Saturday after the visitors had fought back from three goals down.
Napoli, runners-up in three of the last four seasons, hit back from conceding a contentious early penalty to win 4-3 at new-look Fiorentina in a hugely entertaining start to their Serie A campaign on Saturday.
But the most emotional scenes came during Fiorentina's 3-1 defeat at Atalanta, who kept their hopes of Champions League football alive thanks to goals from Josip Ilicic, Alejandro Gomez and Robin Gosens.
Mohamed Salah's delightful first-half strike gave Liverpool a 1-0 win over Napoli at Anfield on Tuesday that sent them into the Champions League's last 16 and the Italian side crashing out.
Big-spending Paris St Germain avoided a defeat that could have derailed their Champions League campaign when Angel Di Maria curled in a delightful stoppage-time equaliser to rescue a 2-2 draw at home to Napoli on Wednesday.
Lorenzo Insigne’s 90th-minute winner gave Napoli a deserved 1-0 Champions League victory over Liverpool on Wednesday that saw the Italians move to the top of Group C.
Senegalese defender Kalidou Koulibaly's stunning last-gasp goal keep Napoli's title hopes alive with a 1-0 win at Juventus closing the gap to just one point on the Serie A champions.
Paulo Dybala strikes twice to send Juventus to the top of Serie A with a 2-0 victory over Udinese as title rivals Napoli are held to a goalless draw at Inter Milan.
