Mignolet saved twice in the shootout, including a brilliant stop to deny Marc Muniesa in sudden death, which allowed Joe Allen to stroke home the decisive spotkick and send Liverpool to Wembley.
It was a fortunate end to an uncomfortable evening for the hosts, who were under pressure for much of the encounter which ended 1-0 to Stoke City after extra time.
Stoke took the lead in first-half stoppage time when Marko Arnautovic swept the ball home from an offside position but the assistant’s flag stayed down and the goal was allowed to stand.
Liverpool struggled to breakdown a resolute Stoke defence and after neither side could add to the scoring for the remainder of the match, it went to penalties and Allen’s effort gave the hosts a 6-5 win in the shootout.
It was a thrilling end for Liverpool manager Juergen Klopp who could not bear to watch as Allen’s final penalty hit the net.
“It was great, the atmosphere was special,” the German told Sky Sports. “It was a good game for my side against a difficult side to play…
“Wembley is a cool place to play football, but we go there to win. It’s not much fun to lose.”
Liverpool will face either Everton or Manchester City in the final on February 28, with Roberto Martinez’s side holding a 2-1 lead heading into Wednesday’s second leg.
For Stoke manager Mark Hughes, there was little consolation to be had other than his side’s positive performance.
“I thought we merited a win,” he said. “We got a win on paper — goodness knows how long it’s been since we won here — but the objective was to get to a Wembley final which we didn’t.”
Having not won at Anfield in any competition since 1959 with 36 fruitless visits in the interim, they were sharp, well-organised and the better team for the majority of Tuesday’s tie.
Liverpool, the record eight-times League Cup winners, struggled to create any chance of note in the first 45 minutes with their forays into Stoke territory frequently ending with a misplaced pass or a timely Stoke tackle.
The visitors got their reward for blunting Liverpool’s attack with a stoppage-time goal that prompted an angry response from the hosts, with Arnautovic having strayed a metre offside when he stroked home Bojan’s cross.
Liverpool’s Firmino rattled the outside of the post shortly after the interval, but Stoke continued pile on the pressure with the hosts’ defence looking increasingly erratic as the encounter wore on.
Stoke almost took the lead in extra time when substitute Marco van Ginkel bustled through and struck the outside of the post, but the most gripping drama was reserved for the shootout.
Former Liverpool striker Peter Crouch had his effort saved by Mignolet and Emre Can struck the post for the hosts before Muniesa’s effort was kept out and Allen stroked home to seal the tie.