The capital club shocked Inter Milan 3-0 at San Siro on Saturday night to leave Juve and Napoli five points adrift and, after the Azzurri managed to narrow the gap with a 4-0 win over Livorno, the Turin club's quest to catch up started poorly.
Sulley Muntari gave Milan the lead after only 19 seconds of play at the Juventus Stadium but Andrea Pirlo soon levelled with a free-kick against his former club.
For a while the game seemed to be heading towards a bad-tempered draw, until Sebastian Giovinco scored from the bench with Giorgio Chiellini compounding Milan's misery after visiting defender Philippe Mexes was sent off after an hour.
Muntari would double his personal tally on the stroke of full time but it was too little, too late for Milan.
Juve's first appointment after the international break takes them to Fiorentina and they will hope Roma and Napoli cancel each other out in their meeting at the Stadio Olimpico.
Milan, however, can only dream of a title challenge after their third league defeat of the season left them floundering in 12th place.
It was always going to be an eventful night in Turin but Muntari ensured it would be a contest inside 20 seconds.
The Ghanaian was aided by Kwadwo Asamoah's poor positioning when sliding Antonio Nocerino's pass underneath an incredulous Gianluigi Buffon.
Juventus' response was furious and immediate and only Christian Abbiati stood between the hosts and their determination to fight back.
The Milan goalkeeper punched an Asamoah rocket over the bar before pouncing on Chiellini's screamer from the edge of the area.
He had longer to think about Juve's next effort, but it was the one that beat him.
In the 15th minute Pirlo stood quietly over the ball while Nigel De Jong argued he had not fouled Carlos Tevez. Moments later he was steering the ball over the wall and home off Abbiati's flapping glove.
Leonardo Bonucci then managed to avoid a red card - escaping with yellow - after headbutting Robinho but three minutes before the break Juve thought they had grounds for a penalty when Kevin Constant nudged Tevez over in the box.
Referee Gianluca Rocchi was not interested and the scores were level at half-time.
Mexes copied Bonucci's antics following the restart, covertly punching Chiellini's shoulder while Rocchi was distracted.
Then in the 53rd minute, Buffon saved Juve from falling behind again when winning a tense one-on-one with the tricky Robinho.
The Bianconeri began to wrest back control of proceedings and substitute Paul Pogba soon stung Abbiati's palms with a swerving strike.
That disappointment prompted Juve coach Antonio Conte to throw Giovinco into the action and one minute and 48 seconds later his decision was justified.
In his first foray forward, the diminutive Italy international dummied two sliding Rossoneri defenders to slam home a magnificent effort.
Milan's challenge continued to fall apart as Mexes earned the red card he had perhaps deserved 15 minutes earlier. Minutes after fouling Giovinco he saw a second yellow for dissent, leaving the visitors a man short and wide open.
The dismissal saw Pirlo lining up another free-kick and, after his attempt clattered off the bar, Chiellini got down to slide home a decisive third for the delirious hosts.
But Juve failed to properly close ranks as full-time drew closer and Muntari was afforded space to drive in a late goal off Bonucci that offered Milan a shred of comfort from their latest league defeat.