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.
A 33-year wait for the league crown looks closer to ending for Napoli
AC Milan's crisis threatens to deepen as the champions head into Sunday's derby with Inter, miles off the Serie A title pace and in a battle to reach next year's Champions League.
Serie A title fever is sweeping Naples as the football-mad city hopes that rampant Napoli will end more than three decades of waiting to be crowned kings of Italy.
Napoli must seize their "unprecedented opportunity" to win the Scudetto after reaching 50 points at the halfway mark of the Serie A season by beating Salernitana, said Luciano Spalletti.
Dazzling duo Victor Osimhen and Khvicha Kvaratskhelia have Napoli dreaming after starring in a five-goal massacre of Juventus which made them clear favourites to claim a first Serie A title in over three decades.
Napoli stamped their authority on the Serie A title race on Friday by thrashing Juventus 5-1 and moving 10 points clear of the chasing pack.
Napoli moved seven points clear at the top of Serie A after Sunday's 2-0 win at 10-man Sampdoria, who paid tribute to deceased greats Gianluca Vialli and Sinisa Mihajlovic.
Napoli's 11-match winning streak and unbeaten start to the Serie A season ended on Wednesday when Edin Dzeko's second-half goal secured Inter Milan a 1-0 victory.
A brilliant header by Napoli striker Giovanni Simeone helped his side to seal a 2-1 win at AC Milan and return to the top of the Serie A table on Sunday.
Liverpool manager Jurgen Klopp said the Reds must "reinvent" themselves after a poor start to the season was compounded by a 4-1 defeat to Napoli in their Champions League opener on Wednesday.
