Simeone on Sunday found goals in the 34th, 62nd and 90+3rd minutes to dash the hopes of a desperate Napoli, who were reduced to 10 men with the sending off of central defender Kalidou Koulibaly in the sixth minute.
Koulibaly fouled Simeone in the sixth minute when the Senegalese was the last Napoli player to block the Argentine just outside the box at the Stadio Artemio Franchi.
The sending off shook Napoli, who were desperate to keep up with Juventus after the defending champions won 3-2 over Inter Milan.
Fiorentina took the lead when Simeone caught a long ball from Cristiano Biraghi before employing a left foot shot from the centre of the box to the centre of the goal.
Simeone got the second goal as he poked home a corner which was poorly cleared by goalkeeper Pepe Reina.
He completed his hat-trick after Federico Chiesa's through ball caught the Napoli defence off-guard and Simeone charged inside the box before beating Spanish keeper Reina.
Napoli took only a single shot at goal in the entire match as Fiorentina ended their three-match winless streak.
"We needed real conviction, enthusiasm and personality to take on such a great side," Fiorentina chief coach Stefano Pioli was quoted as saying by the club's website.
"We did well to win the foul that led to the sending off, then we really took advantage of our man advantage. There was good character to our play. We came close to perfection -- there are no perfect games, but this came very close in my opinion.
"We're delighted and it's right that we're pleased because we hadn't beaten Napoli at home in nine or ten years. That said, as of Tuesday we need to get our feet on the ground and focus on our recovery because we need a good run-in. We've done a fantastic job so far so now it's all about staying focused."
Napoli head coach Maurizio Sarri told his club's website: "The sending off and their first goal knocked our confidence. I don't know what happened, because in the past we've always stuck together as a team and fought back. We lost our unity today and let the adversity get the better of us."
(This story has not been edited by Social News XYZ staff and is auto-generated from a syndicated feed.)
