The Serie A champions and leaders needed extra time to overcome their rivals, but sealed a comeback victory to advance into the last-four of the competition
The Bianconeri fell behind early to Stephan El Shaarawy's strike, but leveled through Sebastian Giovinco before Mirko Vucinic decided the game in extra time.
The crowd at Juventus Stadium was treated to a frenetic start to the quarterfinal clash, as both teams pushed forward in search of an early opener. Massimo Ambrosini was the first man to take aim at goal, his early snapshot pushed over the bar by Marco Storari with barely two minutes on the clock. It was a warning for Juventus, and one the home team failed to lead as it fell almost instantly behind.
Kevin Prince Boateng stretched the home defense with a storming run down the left flank, and did enough to turn in a low cross from the byline. Giampaolo Pazzini was intelligent enough to let the ball run, and it was El Shaarawy who took full advantage as the Serie A top scorer curled a well-taken effort past the flailing Storari and into the corner of the net. Milan's attacking prowess could not hide certain deficiencies at the back, however. Alessandro Matri had a golden chance to level proceedings after connecting with a cross from Sebastian Giovinco, but unmarked the goal-starved striker nodded wide.
Fortunately for the hosts, that miss was a minor blip on their way to an equaliser. Francesco Acerbi was the villain for Milan. Having given away possession, he compounded his error by felling Matri on the edge of the area. A marvellous free kick from Giovinco gave Marco Amelia no chance, and with just 12 minutes played Juve was back on level terms at 1-1.
Milan continued to press in search of the lead, but in truth was rather lucky to enter halftime level both on the scoresheet and in terms of personnel. Giovinco was handed another chance to strike from a dead-ball situation, but this time Amelia was attentive and pulled off a spectacular save to tip the effort over. The youngster then failed to capitalize on Acerbi's scuffed header that put him clean through against Amelia, firing wide on his left foot. Phillippe Mexes, meanwhile, pushed his luck by obstructing Storari having already earned a booking for a vicious challenge, but to Juve's chagrin he was pardoned and stayed on the field as the first half finished.
The game continued in the same open, high-octane fashion after the interval, and Giovinco again had the chance to put his side in the ascendancy. The striker took advantage of a fortuitous deflection to let loose from short range, but he failed to make decent contact and Amelia had little problem in saving down low. At the other end Boateng also troubled the keeper, forcing Storari to get down and stop a decent effort from distance.
As extra time loomed both teams appeared to lower their tempo, playing more cautiously in anticipation of either an additional 30 minutes, or a decisive strike coming on the counter. Teenage Milan substitute M'Baye Niang briefly raised pulses with a mazy run that was finally ended on the edge of the area with a flawless interception by Leonardo Bonucci. In the dying minutes Niang again went close as his header squeezed wide of the post, but at the final whistle the game remained deadlocked at one apiece.
The match had barely kicked off for 30 minutes of added time before Juve pushed itself into the lead for the first time. Emanuele Giaccherini did well with a tireless run to spearhead the break, and his deep pass rebounded into the path of Vucinic, who made no mistake in finishing from close range. Milan desperately threw itself into attack in search of a way back into the match, but was frustrated in its onslaught by a determined backline and the heroic Storari as it bid farewell to the Coppa Italia.
The victory books Juve's place as the second team into the semifinals, where it joins Lazio, which entered the last-four thanks to a dominating 3-0 victory over Catania.