Juventus, which has won the trophy a record 13 times — including four of the past five editions, will face either Roma or Parma.
The Bianconeri made a number of changes with Cristiano Ronaldo out with illness and Merih Demiral injured.
Dybala and Gonzalo Higuaín combined for the opening goal in the 16th minute, exchanging a series of passes before Higuaín finished it off.
Dybala got on the scoresheet himself 10 minutes later with a powerful penalty after Udinese goalkeeper Nicolas had tripped Federico Bernardeschi.
Higuaín thought he had doubled his tally early in the second half but it was ruled out for offside after a video review.
Instead it was Dybala who got his second minutes later with a shot into the top left corner.
Douglas Costa converted another penalty in the 61st following a handball from Udinese defender Bram Nuytinck.