But Rafael Benitez's men failed to build on their lead and paid the price less than ten minutes from the end when Genoa won a freekick after a foul by Dries Mertens which earned the Belgian a yellow card.
Calaio was handed the honours and from nearly 30 metres out stepped up to curl the ball over the wall and in off Pepe Reina's post as the Spanish goalkeeper looked on in shock.
Instead of reducing the gap to second-placed Roma to four points, Napoli are now six behind Rudi Garcia's men, who themselves are nine behind leaders Juventus albeit with a game in hand.
The hosts broke the deadlock through striker Antonio Cassano six minutes from the interval although only two minutes later Juan Cuadrado got on the end of Alessandro Matri's delivery to beat goalkeeper Antonio Mirante to level.
The visitors suffered another blow two minutes later when Modibo Diakite, who had been booked just before the half hour for a foul from behind on Cassano, saw red after another foul on the former Inter and AC Milan striker.
Despite being a man down Fiorentina pressed forward looking for an equaliser and when the visitors won a late free kick Fernandez spoiled the Parma party with a superbly-struck curling effort which had Mirante scrambling back into his own net.
Parma brought Raffaele Palladino off the bench and he flashed a header wide of the goal within a minute of coming on.
The match finished level, but on a sour note after a scuffle between Borja Valero and Gianni Munari led to both players being sent off in the fourth minute of added-on time.