Yet after making an early save from Babacar, the 34-year-old was unable to prevent a cross from Ante Rebic bouncing in off the frame of his goal following a deflection.
Gonzalo Rodriguez then netted with a sublime back-heeled effort.
Babacar got on the scoresheet with a chipped penalty before Mario Suarez stole the ball and slotted past Zappino with ease.
After the break, Fiorentina understandably eased the pressure on their mismatched opponents, eventually allowing Frosinone midfielder Alessandro Frara a late consolation goal.
Maurizio Sarri's Napoli are fourth, two points behind Fiorentina after a frustrating 0-0 draw at Genoa. Napoli had won their five previous league fixtures, but benched Lorenzo Insigne following his outburst after being substituted in their midweek clash with Palermo.
The home side had goalkeeper Mattia Perin to thank as he made some remarkable saves to keep Napoli at bay, Jose Callejon testing him early on before Dries Mertens struck the post.
It was a hard-earned point for Genoa, particularly as they lost both Blerim Dzemaili and Ezequiel Munoz to injury in the first half.
After the restart, Sarri introduced both Insigne and Manolo Gabbiadini in search of a winning goal, but it never came.
"We created many scoring opportunities, it's just a shame about the result," a disappointed Sarri said.
Meanwhile, Bologna notched only their third win of the campaign, seeing off Atalanta 3-0 thanks to goals from Emanuele Giaccherini, Mattia Destro and Franco Brienza.
On Saturday, Inter downed 10-man Roma 1-0 with Gary Medel scoring the game's only goal, meaning they now trail Fiorentina in the table only by virtue of their inferior goal difference.
Reigning champions Juventus beat Turin rivals Torino 2-1 thanks to an injury time winner from on-loan Chelsea winger Juan Cuadrado.
In Sunday's late game, Sinisa Mihijlovic's AC Milan notched their third consecutive victory away to Lazio to go into sixth place.
The Rossoneri ran out 3-1 winners at the Stadio Olimpico thanks to goals from Andrea Bertolacci, Philippe Mexes and Carlos Bacca.
- AAP