Mattia Destro had put the visitors ahead but goals in the final seven minutes from Gonzalo Rodriguez and the Spanish winger dealt a devastating blow to Filippo Inzaghi
The hosts had fallen behind at a sodden Artemi Franchi when Mattia Destro rewarded under-pressure Filippo Inzaghi's decision to reinstate him to Milan's starting line-up.
However, winger Joaquin, introduced at half-time, helped to turn the tide for Montella's men as he produced a delightful cross for Gonzalo Rodriguez to head home seven minutes from time.
Fiorentina - missing the likes of David Pizarro, Mario Gomez, Stefan Savic and Giuseppe Rossi due to injury - looked to be tiring prior to their equaliser after a hectic run of fixtures including Europa League and Coppa Italia commitments.
However, they continued to press and were rewarded when Joaquin headed home Manuel Pasqual's delivery late on to bolster their hopes of European qualification.
Inzaghi's men were left to lament their inability to see the game out as they succumbed to late goals in back-to-back Serie A outings, with questions about the former striker's future in the Milan hotseat bound to follow.
A Milan win would have truly been a smash-and-grab effort with Fiorentina controlling much of the contest and going close early with a fierce Josip Ilicic effort six minutes in before Keisuke Honda blasted Milan's first opening at Neto.
Honda was played through on goal after some slick build-up with Jeremy Menez next to break through, only to see his shot deflected behind by Aleandro Rosi.
Jose Basanta had the best chance of the opening half-hour, crashing Ilicic's free kick against Diego Lopez's crossbar from close range and Fiorentina continued to knock on the door when the second half eventually resumed amid torrential rain.
The lack of a quality final ball continued to hold back Vincenzo Montella's men, although substitutes Milan Badelj and Joaquin did go close to the opener before the hour mark.
Greatly against the run of play, Milan then got themselves in front when Destro diverted Giacomo Bonaventura's wayward effort past a helpless Neto following a quick break.
Destro's second goal for the San Siro club failed to halt the hosts' advances and incessant Fiorentina pressure finally paid off in the 83rd minute as Rodriguez rose to nod Joaquin's cross home.
And Milan's misery was compounded a minute from the end of normal time as Joaquin was left free to head beyond a helpless Lopez, leaving Inzaghi clinging to his job as his side well adrift of the race for Europe.