Midfielder Joe Allen was the penalty shoot-out hero as his spot-kick sent Liverpool to Wembley after a tense Capital One Cup semi-final second leg at Anfield.
The second-half substitute, who had scored in his previous two midweek outings, slotted home after much-maligned goalkeeper Simon Mignolet had saved Stoke defender Marc Muniesa’s effort in sudden death.
There was some irony the decisive moment was produced by one of the smallest players on the pitch in a match which manager Jurgen Klopp had predicted just before kick-off would be “a heading festival”.
The ball certainly saw some air time but four shots on target in 120 minutes underlined the lack of quality in the game and penalties were almost inevitable from the moment Marko Arnautovic struck a controversial offside goal in the first half.
However, Liverpool extended to 42 occasions their proud record of never having been knocked out when returning to Anfield with a first-leg lead.
They have also never lost the home leg of a League Cup semi-final and have reached a record-extending 11th final, from which they have returned victorious eight times.
Stoke have still to win at Anfield since 1959, which includes 31 defeats and five draws, but this was just about as close as you could get.
They fielded five outfield players at 6ft-plus to Liverpool’s two and it seemed they would target Liverpool’s weakness at set-pieces.
Former Reds striker Peter Crouch, head and shoulders above his markers at 6ft 7ins, won virtually everything in the air but Liverpool, with Lucas Leiva at the forefront, did a reasonable job of mopping up the second ball.
But the hosts were undone seconds before the interval with a move through the middle of the pitch which picked out Bojan Krkic and, with left-back Alberto Moreno nowhere to be seen, he slid a pass across to the unmarked Arnautovic who side-footed home despite replays indicating he was offside.
It was the first shot on target in the game and the sixth time in 2016 Liverpool had conceded from such.
Jon Walters and Bojan both had chances for the visitors but Liverpool, holding a 1-0 lead going into the second leg, seemed reluctant to shoot with Adam Lallana and James Milner both guilty of passing inside the penalty area, although Emre Can and Jordan Henderson had attempts from distance.
Early in the second half Roberto Firmino forced Jack Butland to tip his shot onto the near post with his foot but Stoke quickly gained control and exerted considerable pressure, with Mamadou Sakho throwing himself at a Walters shot an example of the desperation.
Striker Christian Benteke replaced Henderson but it was Sakho who wasted a good Milner free-kick by heading wide, with Benteke failing to meet Moreno’s cross under pressure from Erik Pieters.
The hosts managed just one shot on target as the match went into extra time, where substitute Marco van Ginkel hit the post just before the end of the first period and forced Simon Mignolet into a save in the second whereas Liverpool failed to test Butland.
Crouch and Germany international Emre Can both failed from the spot – but with Walters, Glenn Whelan, Ibrahim Afellay, Xherdan Shaqiri and Van Ginkel scoring for Stoke and Lallana, Benteke, Firmino, Milner and Lucas on target for the hosts, Allen struck after Muniesa failed.