But with time running out Gobbi struck to earn Parma a share of the spoils. They stay 14th, below Atalanta on goal difference, with Fiorentina remaining fifth.
La Viola had gone behind at the stroke of half-time to a deflected Gargano strike that left Neto no chance.
Fiorentina seemed a completely different team after the break and turned it around with Rodriguez soaring above the crowd to nod in a Borja Valero corner.
Then Vargas marked his comeback with what he thought was the winner, chesting down a David Pizarro cross and spinning round for the left-foot volley at full stretch, aided by a slight deflection to beat Antonio Mirante at the near post.
However, Parma would not give up and snatched a point with the last kick of the game, silencing the Stadio Artemio Franchi crowd.
Jonathan Biabiany burst down the right and chipped up a cross to the back post where ex-Fiorentina man Massimo Gobbi nodded in from point-blank range.
It’s another setback for Montella’s men, who were beaten 2-1 at San Siro after taking the lead against Inter on Thursday night.