A late goal by striker Arkadiusz Milik -- assisted by United States attacker Timothy Weah -- sent Juventus into the final of Coppa Italia with a 3-2 aggregate win over Lazio despite a 2-1 defeat in the second leg of their semi-final on Tuesday.

Juventus beat Lazio 2-0 at home in the first leg but forward Valentín Castellanos levelled the tie when he scored twice by the 48th minute, before substitute Milik netted the decider from close range seven minutes from time.

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Record 14-times winners Juventus, who lifted their last trophy to date when they won the Italian Cup in 2020-21, have reached their 22nd Coppa Italia final.

"Lazio had to turn the game around, it was normal to expect aggression," Juventus coach Massimiliano Allegri told a press conference. "After the 2-0 at the start of the second half we improved and we got the result against an excellent Lazio. [But] we should have scored first.

"Today was an important match. Our elimination would have led to a dangerous psychological repercussion given that we are not yet mathematically [qualified for] the Champions League."

Lazio were quick to revive the fans' hopes for a turnaround from the first leg's deficit when Castellanos outjumped the Juve defence to give the hosts the lead on the night with a towering header in the 12th minute, nodding home a Luis Alberto corner.

He could have scored the second just before half-time, when he broke into the area after latching on to another neat pass by Alberto, but Juve keeper Mattia Perin kept his low shot out.

However, Castellanos made no mistake after the break when Alberto teed him up just outside the box and the Argentine sent the ball low past Perin and into the net to level the tie.

That shook Juventus up and Dusan Vlahovic had two close chances soon after, before Milik struck from point-blank range to book the spot in the final.

Filip Kostic sent a long cross from the left and across the face of the goal for Weah, who squared the ball to Milik and the Poland striker finished with a tap-in two minutes after entering the pitch.

Atalanta host Fiorentina in the other semifinal on Wednesday after the Viola earned a 1-0 advantage in the first leg.

The final will be played at Stadio Olimpico on May 15.