Serie A: Milan 0 Fiorentina 2
Juan Manuel Vargas' deflected 27th-minute free-kick set the visitors on their way, the ball clipping the shin of Sulley Muntari in the wall before spinning beyond a wrong-footed Gabriel.
Milan pressed hard in the second half but Borja Valero tapped home from close range with 17 minutes left to put the result beyond doubt as Fiorentina sealed their third successive win against their hosts at San Siro.
Allegri’s side have now lost five of their opening 11 league matches and seemingly already face an uphill battle to climb towards the UEFA Champions League places.
They made just one change to the side that drew 1-1 with Lazio in midweek, as Kevin Constant replaced Mattia De Sciglio, while Fiorentina made five alterations. The suspended Juan Cuadrado was forced to miss out following his sending off against Napoli on Wednesday, with Spanish winger Joaquin among those dropping to the bench.
It took quarter of an hour for either side to fashion any sort of chance, Cristian Zapata powering his header over the crossbar from six yards after running on to Kaka's corner at pace.
As the half wore on, the game began to open up and the hosts looked more threatening, Kaka feeding Muntari on the edge of the box after 21 minutes, but the Ghanaian's weak shot was comfortably saved by Neto low down to his left.
Six minutes later, the visitors took the lead with their first effort of note.
Vargas' driven free-kick from 25 yards took a deflection off Muntari standing in the wall, with the ricochet diverting the ball's path just enough to defeat Gabriel - who had set off the other way - to nestle in the bottom left-hand corner.
There were few chances of note for the remainder of the half, and the opening 15 minutes of the second half proved similarly uneventful, notable only for a booking for Mario Balotelli when the Italy international shoved Neto to the floor as the goalkeeper shielded the ball out of play.
The incident was one of several altercations between Balotelli and Fiorentina's players, the striker cutting an increasingly frustrated figure as Milan failed to break down their opponents.
And with time running out Valero added to Milan's woes, slotting home from six yards after Gabriel had parried substitute Joaquin's right-wing cross into his path.
Ryder Matos went close to adding to the misery for the hosts, sending an effort a yard wide from the edge of the box with five minutes to go, but it mattered little as Fiorentina comfortably held on to heap the pressure on Milan and Allegri.