The home side looked set for comeback win, but a late goalkeeping blunder forced the Viola to settle for a draw
Vincenzo Montella’s men have won just once in their last four Serie A matches after starting the season with back-to-back victories.
Walter Gargano opened the scoring for the visitors when his left-footed shot from just inside the box took a favourable deflection off a defender, beating a helpless Neto.
The hosts tied the game in the 64th minute when centre-back Gonzalo Rodriguez headed home a corner kick at the near post, then took the lead in the final 15 minutes when Juan Vargas’ shot deflected past Parma goalkeeper Antonio Mirante.
The hosts failed to hold on, however, as Jonathan Biabiany's ball eluded a helpless Neto, allowing Massimo Gobbi to head home at the far post.
Conceding late has become a bad habit for Fiorentina, who allowed 89th-minute equaliser against Cagliari two weeks ago and blew a 1-0 lead at Inter midweek in the final 20 minutes, losing the game by a score of 2-1.
The draw sees Fiorentina sit fifth in Serie A with 11 points, while Parma extend their unbeaten run to three games.