The Portuguese superstar had a first-half penalty saved by Gianluigi Donnarumma in the opponent's goal, but AC Milan's inability to score means Juventus reached the final of the Coppa Italia on away goals rule.
After a three-month absence, Italian football resumed on Friday in the second leg of the semi-final tie after both giants shared a 1-1 draw at the San Siro in the first leg way back in February.
An action-packed first half ended at the Allianz Stadium with the sides locked at 0-0 on the day, and 1-1 on aggregate.
All the drama happened in five first-half minutes, with Cristiano Ronaldo hitting the base of the post from the spot after Juventus were awarded a penalty by VAR for a harsh handball call against Conti in the 16th minute.
Ronaldo has blasted home 21 goals in only 22 Serie A games this season. Still, he couldn't open his Coppa Italia account, with goalkeeper Donnarumma getting the slightest of touches on the striker's spot-kick.
Eighteen seconds later, the visitors were reduced to ten men after Ante Rebic was red-carded for a high-footed challenge on Danilo. But Juventus were unable to capitalise on the man advantage as the half wore out.
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Milan took up a defensive position after that misfortune, but the away goals rule meant that Stefano Pioli's men required a goal to avoid elimination.
The visitors had failed to win against Juventus in the Coppa Italia since 1985, losing eight and drawing five of the 13 meetings since then, and it continued after the final whistle.
On a night when Milan needed just one goal, goalkeeper Gianluigi Buffon didn't have to make a single save as a composed Juventus held off their toothless guests.
Juventus had won the Coppa Italia a record 13 times, including four years in a row before Lazio ended their dominance last season. Only Napoli or Inter Milan (the two teams play tomorrow) now stand in between the Old Ladies and a historic 14 Coppa titles.
