From the beginning in Milan, Juve survived a few threats before reaching the final for the second season.
Romelu Lukaku and Achraf Hakimi, former Manchester United, missed presentable openings for the visitors.
Two excellent saves from Samir Handanovic refused Cristiano Ronaldo.
In the first leg Inter took lead in Argentina’s strike Lautaro Martinez, but in a nine-minute spell, Portugal’s lead Ronaldo scores two times.
The second semi-final winners from Atalanta and Napoli who are in the draw on the 0-0 after the first leg Wednesday will be met by Juve in the finals on 19 May.
Napoli defeated Juventus 4-2 in a penalty shootout at the Coppa Italia final last season.