Antonio Conte's men held onto the lead until the break, but the Nerazzurri were gifted a route back into the game when Claudio Marchisio tugged Milito's shirt in the area, pulling him off balance as he shaped to shoot.
The referee pointed to the spot and the Argentine stepped up himself to take it, firing confidently beyond a despairing Gianluigi Buffon.
Inter took the lead when Buffon could only parry Fredy Guarin's shot into the path of Milito, who gleefully tucked the ball away to put the visitors on course for a famous victory.
The Bianconeri pushed forward in the final stages, with Marchisio and Fabio Quagliarella both going close.
However, the visitors went on to kill the game with a third goal, with Rodrigo Palacio scampering through to slot past Buffon.