A 2-1 victory at Selhurst Park sealed progression, with Ismaila Sarr striking just after half-time to settle the tie after Shakhtar briefly threatened a comeback. Daniel Munoz had earlier forced an own goal to give Palace the lead on the night, before Eguinaldo's superb effort levelled things.
Palace had already taken control with a 3-1 first-leg advantage and rarely looked under serious threat. Yeremy Pino also had a goal ruled out for offside, while Jean-Philippe Mateta hit the post in a dominant first-half display.
Sarr's goal - his ninth in the competition this season - ensured there would be no late drama as Oliver Glasner's side closed out a historic night in style.
The result caps a remarkable period for Palace under Glasner, who will leave in the summer after guiding the club through their most successful era, including last season's FA Cup triumph.
"This is a huge achievement," Glasner said. "If you stick together in difficult moments, you get the reward."
Captain Dean Henderson praised the connection between players and fans, calling it "incredible" and crediting the manager for building belief in the squad.
Midfielder Adam Wharton added: "It's an incredible feeling I'll never forget. The atmosphere was unbelievable and it means everything to the club."
Palace's route to the final has included extensive European travel after their Conference League placement, taking in fixtures across multiple countries before reaching Leipzig.
They now face Rayo Vallecano, who defeated Strasbourg in their semi-final, in a final that offers Palace the chance to secure a first European trophy and cap a defining season in the club's history.
