Eden Hazard easily knocked in the game-winner in what could be the Belgian star’s last game at Stamford Bridge in a Chelsea kit.
The game resorted to the shootout after the two-legged semifinal finished 2-2 on aggregate.
The Blues will face their London rivals in the final in Baku on May 29.
Chelsea settled down and took the lead in the 28th minute, when Ruben Loftus-Cheek had time to slip the ball past Frankfurt goalkeeper Kevin Trapp after an initial release down the left flank by Eden Hazard.
Following the break, Eintracht quickly regrouped to equalised in the 49th minute when Luka Jovic got behind Chelsea’s backline for a composed shot past Kepa.
Both sides had solid chances to break through for the game winner but ultimately were unable to get a second goal, sending the match into added extra time.