Juve did manage to equalise before half time, however, when the experienced Pirlo curled in a free kick past the despairing Christian Abbiati in the Milan goal.
The Bianconeri almost took the lead in the second half when Paul Pogba let loose with a fierce strike that Abbiati did well to keep out.
Despite the Milan goalkeeper's efforts, the home side finally took the lead through Sebastian Giovinco. He scored after having been on the pitch for only two minutes by jinking past Cristian Zapata before firing his shot low into the net.
Juventus then completed their victory following the dismissal of Philippe Mexes, as Chiellini followed up from Pirlo's free kick to make the score 3-1.
As the game entered the final stages, Milan grabbed one back through Muntari, whose shot beat Buffon after a deflection.