Arkadiusz Milik's late strike helped Juventus reach the Italian Cup final on Tuesday with a 3-2 aggregate win over Lazio despite losing a tense second leg 2-1.

Nursing a 2-0 first-leg win, Juventus found themselves 2-0 down on the night and completely dominated as Lazio made a fight of it with a brace of goals from Valentin Castellanos.

But late Juventus substitute Milik scored with his first touch on 83 minutes to settle Juve's nerves and the two-legged semi with a prod-in.

The Turin side will play either Atalanta or Fiorentina in the May 15 final, with the Florence outfit leading 1-0 before Wednesday's return leg.

"We suffered against a good side, so we're happy to be in the final," said the Polish striker Milik.

"We know we have to play better in the final, and we know we can play better."

Mattia Perin was in the Juventus goal as their Cup 'keeper, and suffered a torrid time with regular starter Wojciech Szczesny watching on from the bench.

Castellanos headed Lazio in front with a thunderous header from a corner on 12 minutes and the Argentinian ran from deep to fire a low shot into the bottom corner shortly after the restart.

Juve coach Massimiliano Allegri brought on forwards Timothy Weah and Milik with the clock ticking down and both were involved as the double change paid immediate dividends.

Juventus are bidding to win the Coppa Italia for the 15th time and despite only two wins in 12 matches are third in Serie A.

"The great satisfaction here is to have reached this final, it will boost us for the end of the league where we still need a few points to qualify for the Champions League," said a relieved Allegri.

Juventus strike partners Federico Chiesa and Dusan Vlahovic produced brilliant finishes in the first leg and the final is at Rome's Stadio Olimpico.