The first leg ended 1-0 in Bergamo thanks to an early Gonzalo Higuain goal, and Juventus won the second when Miralem Pjanic slotted in a 75th-minute penalty awarded after Blaise Matuidi was fouled in the box.
The three-time holders will play either AC Milan or Lazio -- who are 0-0 going into the second semi-final later on Wednesday in the Stadio Olympico -- in the final which will be in Rome on May 9.
Massimiliano Allegri's Juventus are bidding for a record fourth successive Cup title and 13th in total.