The Reds took a one-goal lead into the semi-final second leg at Anfield after defeating the Potters at the Britannia Stadium earlier this month.
Jurgen Klopp's preserved his perfect semi-final record despite his side conceding on the stroke of half-time before Mark Hughes' men held out to lead 1-0 at the end of extra-time.
The Potters were the more creative of the two sides throughout before the Reds pushed for a winner later in proceedings but the contest was forced into penalties as it ended 1-1 on aggregate after 180 minutes of regular time and 30 minutes of exra-time.
The much-maligned Simon Mignolet was the hero for the Reds by making two saves when keeping out Peter Crouch and Marc Muniesa while Emre Can hit the outside of the post with Liverpool's second attempt from 12 yards.
In the end, midfielder Joe Allen finished emphatically in sudden death of the shootout to give the Reds a 6-5 triumph, sending them to Wembley on February 28 where they will meet the winner of Wednesday night's meeting between Manchester City and Everton.
2015/16 CAPITAL ONE CUP - SEMI-FINAL 2nd LEG
*Aggregate 1-1. Liverpool win 6-5 on penalties
Anfield, Liverpool - 43,091