Ahead of kickoff, the onus was on second-placed Napoli to triumph at the Stadio Artemio Franchi after the Old Lady beat Inter Milan 3-2 on Saturday to open up a four-point gap at the top.
Napoli were hamstrung from the opening stages of the encounter as Kalidou Koulibaly was sent off on eight minutes for denying Simeone a clear goalscoring opportunity just outside the box.
Simeone then grabbed his and Fiorentina's second on 62 minutes as a corner kick which caused havoc in the Napoli defence culminated in the 22-year-old striking home on the rebound.
The Atletico Madrid manager's son went on to claim the match ball with an injury-time third, running on to a through-ball, shrugging off Mario Rui and placing the angled drive past Reina.
FIORENTINA (4-3-3): Sportiello; Laurini (Gaspar 62'), Milenkovic, Pezzella, Biraghi; Veretout, Badelj (Cristoforo 83'), Benassi; Saponara (Eysseric 74'), Chiesa; Simeone
NAPOLI (4-3-3): Reina; Hysaj, Albiol, Koulibaly, Rui; Allan, Jorginho (Tonelli 10'), Hamsik (Zielinski 57'); Callejon, Mertens (Milik 57'), Insigne