Extra-time substitute Tsimikas sent Edouard Mendy the wrong way with the decisive kick after Alisson saved from Mason Mount, as Jurgen Klopp's side secured a repeat of February's Carabao Cup final win after two hours of action ended 0-0.
Liverpool was dealt a huge blow when Mohamed Salah was forced off through injury in the first half, with Virgil van Dijk and Andrew Robertson also substituted after 90 minutes were through.
But the Reds dug deep to condemn Chelsea to a third consecutive FA Cup final loss, and they could yet add the Premier League and UEFA Champions League trophies to their domestic cup double in the coming weeks.
