Napoli could not keep step with their Scudetto rivals from Turin as Maurizio Sarri’s men left the pitch in tears after the final whistle.
The hero from last week Kalidou Koulibaly turned into the villain here after the defender was given his marching orders for a foul on Simeone with just eight minutes on the clock.
The son of Atletico Madrid boss Diego drove Cristiano Biraghi’s through ball beyond Pepe Reina in the 34th minute to give the home side the lead.
Simeone later doubled their advantage and his tally for the evening when Milan Badelj’s headed attempt fortunately rebounded straight to his feet.
The 22-year-old compounded Napoli’s woes and capped off a memorable day for himself in the dying moments of the match.
He latched on to a pass from Federico Chiesa before slotting past Reina to seal his hat-trick deep into second-half stoppage time.
It was the first time Fiorentina had won in four games while Napoli remain second but four points behind Juventus with just three games remaining.