The win leaves second-placed Inter one point behind champions and league leaders Juve and is a sign that Andrea Stramaccioni's side are genuine challengers for the title.
"It hurts to lose, obviously it hurts, but it's right to give credit to Inter, who played in a very intelligent way, with a great will to win," said Juventus captain Gianluigi Buffon.
"I conceded three goals without having all that much to do but that can happen against the players that Inter have, they're very good."
Juve scored straight from the kick off when Kwadwo Asamoah latched onto Mirko Vucinic's through ball and scuffed his shot into the path of Arturo Vidal, who gleefully tapped home from the edge of the six yard box after 19 seconds.
Television replays showed Asamoah was offside when he collected Vucinic's pass but the linesman's flag stayed down.
"We were caught napping for the first goal, even if it was offside, but after that we reacted and played brilliantly. We deserved to win," Milito told Sky Sport Italia.
"It was a really hard match. We knew that it would be like that, we were up against the current champions, a great team like Juventus."
Juve could have doubled their lead after eight minutes when Claudio Marchioso met Andrea Pirlo's delightful through ball with a volley that Samir Handanovic did well to push wide.
Inter must have expected a torrid evening but were unlucky not to level three minutes later when Rodrigo Palacio's header from Esteban Cambiasso's freekick was ruled out for offside.
Inter were giving Antonio Conte's side their toughest game yet but Handanovic saved them from ending the first half two goals down, saving from Vidal who was clean through on goal.
They went close again three minutes later when Yuto Nagatomo forced a fine save from Buffon after dribbling past two defenders in the box, but Andrea Stramaccioni's side got the equaliser they deserved just before the hour mark.
The Argentine piled on the agony for the champions with a quarter-of-an-hour left when Fredy Guarin's powerful shot was pushed straight into his path by Buffon, who could only watch as Milito gobbled up the chance to make it 2-1 to the visitors.
