Gobbi's late goal saves Parma
Parma had not scored in its previous three games in Florence, but took the lead on the stroke of halftime when Walter Gargano's shot was deflected over the prone Fiorentina goalkeeper Neto.
Fiorentina leveled in the 64th minute when Gonzalo Rodriguez leapt highest at the near post to head a corner across into the right side of the goal.
The hosts went ahead 12 minutes later when Juan Vargas did well to control the ball between two Parma defenders before turning and firing past Antonio Mirante from close range.
But seconds from fulltime, Gobbi headed in Jonathan Biabiany's cross to earn a competition point for Parma.
''There is bitterness, disappointment,'' Fiorentina coach Vincenzo Montella said. ''In the first half we didn't do very well, partly down to the great work of Parma, while I saw a different Fiorentina after the break.
''We had a different tempo and style, which is why we deservedly went in front. We really should have won the match, we should have kept the ball, instead we kept trying to break them down and we conceded a goal.''
There was more bad news for Fiorentina as striker Giuseppe Rossi - who has scored six goals in seven matches since returning from almost two years of injuries - was forced off with a muscle injury in the 36th.
It is another blow for the the U.S.-born forward who would have been hoping for a recall to the Italy squad for the upcoming World Cup qualifiers against Denmark and Armenia.
Fiorentina remains fifth, seven points behind early leader Roma. Parma is 14th.
It was an end-to-end match and Alberto Aquilani almost scored a stunning opener in the 22nd minute with an overhead kick which went just past the left post. Rossi also headed narrowly past the left upright moments later.
Parma should have gone in front in the 25th but Raffaele Palladino fired straight at Neto.
Fiorentina missed a chance on the hour mark when Mirante pulled off a great save to deny Marcos Alonso.