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.
Khvicha Kvaratskhelia helped put Napoli's Serie A title defence back on track with a brace in Saturday's 3-1 win at Verona which moved the champions four points behind leaders AC Milan.
Real scored the winner in the 78th minute as a stunning long-range shot from Federico Valverde cannoned off the crossbar straight onto the back of the flailing Meret's head before deflecting into his own goal.
Inter Milan laid down an early title marker on Saturday by handing out a 5-1 derby hammering to AC Milan and going it alone at the Serie A summit, while champions Napoli were held 2-2 at promoted Genoa.
Victor Osimhen netted his third goal of the season from the penalty spot 15 minutes into Napoli's first home match since lifting the league title in front of their fans for the third time back in June.
Victor Osimhen started where he left off for Napoli with a brace in Saturday's 3-1 victory at promoted Frosinone which gave the champions a winning start to their Serie A title defence.
Napoli ended their 33-year wait for a Serie A title last season in spectacular fashion by securing it with five games to spare, but with new management and recent history against them, retaining it could be a very tough task. They begin their title defence at promoted Frosinone on Saturday.
Luciano Spalletti will be the new head coach of Italy's national soccer team, the country's football federation said on Friday, replacing Roberto Mancini who resigned on Aug 13.
The Italian Football Federation and Luciano Spalletti have reached an agreement for him to succeed Roberto Mancini as coach of the national team, according to reports in the Italian press on Friday.
South Korea defender Kim Min-jae has joined German side Bayern Munich on a five-year contract from Serie A champions Napoli, the Bundesliga club said on Tuesday.
Ex-Roma boss Garcia, 59, takes over from Luciano Spalletti who left his position after guiding the southern club to their first Scudetto in 33 years.
