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.
Former Chelsea and Tottenham coach Antonio Conte was hired by Napoli on Wednesday as the deposed Serie A champions try to bounce back from their disastrous league title defence.
Empoli, who are battling relegation, opened the scoring after four minutes when striker Alberto Cerri headed in a close-range cross for what proved to be the winner.
"We're not mathematically out of it but the chances of us getting there are very slim," said Calzona after his first league defeat as Napoli boss
Italian club Napoli said they were "stunned" after Italy's football federation (FIGC) on Tuesday dropped a probe into alleged racist comments made by Inter Milan's Francesco Acerbi to Napoli's Juan Jesus due to lack of evidence.
Barcelona came flying out of the blocks with goals from Fermin Lopez and Joao Cancelo but after Amir Rrahmani pulled one back, the Catalans started to sweat.
Nigeria forward Osimhen rolled home the leveller with 15 minutes left of the first leg of their Champions League last 16 tie at the Stadio Diego Armando Maradona, in his first match since returning from the Africa Cup of Nations.
The 62-year-old Mazzarri became the second man to be sent packing this season by the ailing Italian champions.
Nigeria striker Victor Osimhen will leave Napoli this summer and join "either Real Madrid, Paris Saint-Germain or an English club", the Italian club's president and owner Aurelio De Laurentiis said on Friday.
Napoli put aside their recent troubles on Thursday by reaching the Italian Super Cup final with a convincing 3-0 win over Fiorentina in Riyadh.
Napoli striker Victor Osimhen has replied angrily to suggestions that he would leave the Serie A side for Saudi Arabia at the end of this season from agent Mamuka Jugeli, who represents club team mate Khvicha Kvaratskhelia.
