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.
Serie A leaders Napoli thrashed Torino 4-0 away with a double from Victor Oshimen and goals from Khvicha Kvaratskhelia and Tanguy Ndombele on Sunday to move closer to the title.
Eintracht Frankfurt coach Oliver Glasner said Wednesday that Napoli are on the same level as Bayern Munich after his team were knocked out of the Champions League by Serie A's runaway leaders.
Napoli forward Victor Osimhen struck either side of the break to steer the Italians to a comfortable 3-0 victory over Eintracht Frankfurt on Wednesday and into the Champions League quarterfinals for the first time.
The 11th goal of the Georgian's debut Serie A season came in the 60th minute of Saturday's game, as he slalomed his way into the penalty area and left defenders floundering before burying a fierce finish into the roof of the net.
Napoli striker Victor Osimhen says if he leads the club to first Serie A title in more than 30 years, he will become a club "icon", but he would not be able to reach the status of late Argentine great Diego Maradona.
Matias Vecino's brilliant long-range strike earned Lazio a 1-0 win at Napoli on Friday as the runaway Serie A leaders lost for only the second time in the league this season.
Osimhen tapped in at the far post to give his team a 40th minute lead
Napoli have had an impressive season so far, currently with a 15-point lead over second-placed Inter Milan in Serie A, and have won seven straight domestic league games, scoring at least two goals in each.
Simone Inzaghi's side stay second and are three points ahead of local rivals AC Milan, who beat Monza 1-0 earlier on Saturday, but are a long way behind rampant Napoli after their 2-0 win at Sassuolo on Friday.
It looks only a matter of time before Luciano Spalletti's rampant side secure a Scudetto dreamed of by Napoli fans since the days of Diego Maradona
