Vincenzo Montella's men looked on course for their third win in four top-flight matches at the Stadio Artemio Franchi this season after second-half goals from Gonzalo Rodriguez and Juan Vargas overturned Walter Gargano's opener for the visitors.
However, former Fiorentina defender Gobbi had other ideas, as his back-post header in the 92nd minute gave Roberto Donadoni's side a point.
Fiorentina spent much of the first half on the front foot, but it was Parma who broke the deadlock in stoppage time before the interval.
Gargano, who joined the club from Napoli in the close-season, had an effort from just inside the area that was heavily deflected, giving home keeper Neto no chance.
Montella's team came out strongly after the break though, and eventually drew level in the 64th minute when Gonzalo glanced a corner home at the near post.
Vargas then appeared to have given Fiorentina all three points with a smart finish 13 minutes later, but Gobbi intervened in the dying seconds to deny them the win.
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