Romelu Lukaku scored one and set up the other for Giacomo Raspadori on Sunday to help Napoli move back to within a point of Inter, who fought back from two down to beat Monza 3-2 on Saturday.
Atalanta proved they are very much among the fray with a statement 4-0 win at fourth-placed Juventus to close the gap on Inter back to three points.
Atalanta's title credentials will be truly tested next weekend when they host the Nerazzurri.
Fiorentina's hopes of making it into the top four diminished after their fourth loss in five league matches.
Napoli also came into the match on a mediocre run, having drawn four of their past five and losing the other.
But the hosts took the lead on 26 minutes following great work from Scott McTominay as he cut inside from the left and unleashed a shot that former Manchester United teammate David de Gea could only parry into the path of Lukaku, who tapped in the rebound.
Giovanni Di Lorenzo hit the crossbar for Napoli as Fiore had De Gea to thank for a number of impressive saves that kept them in the match.
Napoli eventually doubled their lead on the hour mark with a team move that ended with Lukaku playing a through ball for Raspadori to sweep home.
Fiorentina pulled one back six minutes later as a backheeled flick from Moise Kean released Albert Gudmundsson to drill low into the near corner.
The match in Turin was a head-to-head battle for third, with just three points separating Atalanta and Juventus.
The league's top scorer, Mateo Retegui, gave Atalanta the lead in the 29th from the spot after US international Weston McKennie was penalised for handball.
It was Retegui's 22nd goal in Serie A this season — seven more than nearest challenger Kean.
A combination of the woodwork and Juve goalkeeper Michele Di Gregorio prevented Atalanta from doubling their lead by halftime but Marten de Roon did get the visitors' second within a minute of the restart after Ademola Lookman's effort was parried.
Davide Zappacosta all but sealed the match in the 66th and Lookman capped a fantastic performance 11 minutes later.
Elsewhere, sixth-placed Bologna continued their fine form with a 2-1 win at 10-man Hellas Verona and Matias Soule scored after only 22 seconds to set Roma on their way to a 1-0 win at relegation-threatened Empoli.
Statistics provider Opta said it was Roma's fastest goal in a Serie A match (since that data started being collected in 2004).
It was a fifth straight win in all competitions for Roma, who visit Athletic Bilbao in the second leg of the Europa League round of 16 on Thursday.
Roma also extended their unbeaten run in Serie A to 12 matches, leapfrogging Fiorentina into seventh.
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