The two sides met in the Carabao Cup final in February which Liverpool won on penalties following a 0-0 draw after extra time.
It is the first time since 1992-93 season that the same two teams have competed in the League Cup final and the FA Cup final.
Liverpool beat Manchester City 3-2 at Wembley on Saturday to book their place in the final.
A resilient Palace side held Chelsea in the first half but were undone by two second half goals from Ruben Loftus-Cheek and Mason Mount.
Chelsea will now contest their third straight FA Cup final after losing the previous two to Arsenal and Leicester City.
"It was not easy because we played three games in three different competitions. It is not always easy, very challenging physically, we are the team with the most minutes in Europe I think, it is also challenging mentally," Chelsea manager Thomas Tuchel told ITV Sport after the game.
"I thought the performance was very controlled and very serious, we took care of their counterattacks. It was hard, the opponent changed system twice, you cannot lose focus for a minute.
"He [Ruben Loftus-Cheek] was very, very strong in matches against Southampton and Real Madrid, he would have deserved to start but we expected a back four. We knew Ruben would have a big impact off the bench. I am very happy.
"He hid his talent and potential for a long time in his career. He is capable of producing performances that everyone sees on the pitch. For him it is step by step that he continues to grow in his confidence."
