The hosts had come from behind to take a 2-1 lead with 12 minutes remaining, goals from Gonzalo Rodriguez and substitute Juan Vargas overturning Walter Gargano's opener.
But Gobbi, a former Fiorentina midfielder, had the last word, snatching a 2-2 draw for the visitors in the 92nd minute.
La Viola headed into the contest looking to return to winning ways after Thursday's 2-1 defeat at Inter Milan - their first loss of the campaign.
Monday's result left Fiorentina unbeaten and kept them in fifth place in the standings. Parma, meanwhile, have collected one win from six games.
The visitors created the first chance in the sixth minute when Mattia Cassani's bullet strike was kept out by Fiorentina goalkeeper Norberto Neto.
Fiorentina responded well and, midway through the first half, Alberto Aquilani's acrobatic volley went wide of the far post.
The hosts should have then gone in front but Giuseppe Rossi's close-range header from Facundo Roncaglia's perfect cross flew off target.
In the 36th minute, Fiorentina suffered a setback with the team's top scorer Rossi having to leave the pitch with a muscular injury.
Parma went ahead on the stroke of half-time. Cassani fed Gargano in the box and his left-footed strike from 12 yards took a slight deflection off a defender and beat Neto.
Fiorentina coach Vincenzo Montella introduced Vargas at half-time and the substitute carried the home side's early attacks.
Vargas' cross flashed across the six-yard box with nobody able to get the necessary touch.
On the hour mark, Marcos Alonso's shot towards the far post forced a diving save from Parma goalkeeper Antonio Mirante.
Fiorentina's efforts paid off in the 64th minute when Rodriguez got his head on Borja Valero's cross and his six-yard effort beat Mirante.
And the hosts went in front when Vargas controlled the ball inside the area and drilled a left-footed shot towards the far post, out of the reach of Mirante.
Parma did not give up, though, and had the last laugh with 10 seconds to go when Gobbi got past his marker and headed Jonathan Biabiany's cross past Neto to earn his team a point.