Joe Allen scored the winning penalty in tense semi-final shoot-out to send Liverpool to the Capital One Cup final.
Stoke defender Marc Muniesa missed the crucial spot-kick for Stoke courtesy of a brilliant save from Liverpool keeper Simon Mignolet.
The Potters, trailing 1-0 from the first leg, had brought the tie level in the first half when Marko Arnautovic tapped in Bojan Krkic's cross which replays suggested to be offside.
They also went close in extra-time when Marco Van Ginkel's shot hit the post, while Liverpool's Roberto Firmino also saw an effort come off the woodwork.
Liverpool will face either Manchester City or Everton - who play tomorrow morning AEDT - in the final at Wembley Stadium on February 28.
Next for the Reds is a home tie with West Ham on Sunday morning AEDT in the FA Cup fourth round and for Stoke, its Crystal palace away in the same competition.
