Star striker Victor Osimhen scored either side of half time before Piotr Zielinski converted from the penalty spot just after the hour mark to ensure the Parthenopeans have their name in the hat for Friday's quarter-final draw.
Despite being banned from attending the Stadio Diego Armando Maradona following unsavoury incidents in last month's first leg in Germany, hundreds of Frankfurt supporters travelled to Naples and clashed with Italian police prior to kickoff, with smoke bombs and flares thrown and cars set on fire.
On the pitch, Frankfurt - who were having to cope without top scorer Randal Kolo Muani following his red card in the first leg - made a bright start to proceedings and appeared to have learned lessons from the first leg, pressing high with aggression and putting Napoli under pressure in their own half.
However, the first decent chance fell to in-demand striker Osimhen in the 15th minute who saw a first-time shot saved low down by Kevin Trapp, before wing wizard Khvicha Kvaratskhelia glided into the final third and fired a strike into the legs of Frankfurt's number one from a tight angle.
Oliver Glasner's side continued to push forward and keep Napoli's backline on their toes, but the Bundesliga outfit lacked a cutting edge in the final third and failed to register a single shot on target in the first half.
Meanwhile, Napoli were in control of the tie, boasting the majority of possession, and found another gear towards the end of the half before Osimhen broke the deadlock with a towering heading in the second minute of stoppage time, connecting with Matteo Politano's floated cross to become the first-ever Napoli player to score in both legs of a Champions League knockout tie.
Despite leading 3-0 on aggregate, Napoli refused to rest on their laurels and came out the blocks quickly in the second half, with their lively start rewarded with a second goal in the 53rd minute.
After receiving a floated cross-field pass from Kvaratskhelia, right-back Giovanni Di Lorenzo fired a low-driven cross into the danger zone for Osimhen to tap home his second of the night from close range.
The Nigerian has now scored 13 goals in his last 12 games since the turn of the year, with his brace against Frankfurt increasing his overall goal tally in the 2022-23 campaign to 23 in 28 games across all competitions.
Frankfurt's night then went from bad to worse 11 minutes later when Djibril Sow was penalised for tripping Zielinski inside the penalty area. Although Osimhen was on a hat-trick, Zielinski stepped up and placed his effort from 12 yards straight down the middle to add a third for the hosts.
Napoli were in cruise control for the final 20 minutes of the contest and barely needed to get out of second gear as Frankfurt's first-half tempo fizzled out after the interval.
Luciano Spalletti's side have now won all four of their Champions League home matches this season, scoring 14 goals in the process, and will be a side that the remaining seven teams in the competition will be keen to avoid in Friday's quarter-final draw.
Napoli will now switch their focus back to Serie A and will attempt to move one step closer to lifting their first title for 33 years when they travel to Torino on Sunday, while Frankfurt will look to dust themselves down and return to winning ways when they face Union Berlin in the Bundesliga.