Napoli got back to winning ways in their newly-named Diego Armando Maradona Stadium after falling to promoted Spezia in its last home match.
Gennaro Gattuso's side came out firing despite the absence of midfielder Fabian Ruiz who tested positive for Covid-19, going four goals up before the break.
"It looked easy but it wasn't," Gattuso said.
"Today we couldn't get it wrong because this year we have already failed too many times at home. We wanted to join Roma, this match was very important for us."
Napoli is level on points with Roma which lost 3-0 to Lazio on Saturday (AEDT).
Insigne got the first goal after just five minutes following good work from Hirving Lozano and Andrea Petagna.
Fiorentina missed three chances to equalise, twice through Cristiano Biraghi, with Napoli keeper David Ospina denying Franck Ribery before the hosts notched three goals in the last nine minutes of the first half.
Petagna found Diego Demme to finish off, with Insigne then bursting through to set up Lozano for the third and Piotr Zielinski adding a fourth before the break.
Fiorentina could find no way past Kalidou Koulibaly and the Napoli defence.
Napoli was awarded a penalty after Gaetano Castrovilli fouled Tiemoue Bakayoko. Insigne converted from the spot for his ninth goal this season.
Substitute Matteo Politano completed the rout with a minute to go as Napoli got a major boost before next week's Italian SuperCup against Juventus.
"It's a difficult game to comment on, six shots on goal and six goals, all unstoppable," said Fiorentina coach Cesare Prandelli.
"I apologise to the fans. The third goal, with Insigne's slalom between five of our players, sums up our game."
In Bergamo, Atalanta mised the chance to move third, dropping points before next week's trip to AC Milan.
Gian Piero Gasperini's side had won their first three matches of the year with a total of 12 goals scored.
Hans Hateboer rattled the post for Atalanta after 65 minutes in the best chance for the host which are sixth, eight points behind AC Milan. Genoa are 16th position, two points above the relegation zone.
European hopeful Sassuolo, in eighth two points behind Atalanta, salvaged a point in a 1-1 draw against 19th-placed Parma.
A Filip Duricic penalty deep into injury time levelled for Sassuolo after Juraj Kucka had headed Parma in front after 37 minutes.
Nigerian Simy scored twice as rock-bottom Crotone earned their third win of the season 4-1 over 11th-placed Benevento in a clash of promoted sides.