Juve now have 21 wins in their last 22 League games, and have extended their lead at the top of the Scudetto to nine points over Napoli, who play on Sunday.
Here's what Bianconeri manager Massimiliano Allegri had to say after the game against his former employers -
"I must compliment Milan for interpreting the game in the best way and were unlucky to find a great Buffon blocking their path.
"I also compliment my own players, as we took a step forward. As time wore on we kept the ball better and didn't run any more risks. We had planned to play off the shoulders of their centre-backs, something that went considerably better after the break.
"We could've played better in some moments. It was a difficult match, because it is never easy to win at San Siro. Milan have good players and it was important we not slow down our progress.
"Any side that wins 21 out of 22 rounds is clearly doing something extraordinary."
Allegri was seen speaking to his opposite number Sinisa Mihajlovic and Milan CEO Adriano Galliani after the game -
"I complimented Galliani and said they have the possibility, as do we, of winning the Coppa Italia and qualifying for the Europa League.
"It's not easy when you have to build a new squad, but I think Milan have the opportunity to soon be fighting for the top three places again.
"I had three and a half wonderful years at Milan and retain an excellent rapport with the President and Galliani."
Paul Pogba, scorer of the winning goal, also spoke to the media after the game, praising the maturity shown by Juventus on the day -
"The title race isn't over yet, we've got to keep on winning.
"Today we did well and proved we are a mature side. It's a deserved victory.
"We work to defend all together. People talked so much at the start of the season, but we had time to come back.
"We realised how important this match was. I am happy for the team and for me."