Caoimhin Kelleher saved two Leicester penalties before Diogo Jota, who was a key figure off the bench, converted the crucial spot-kick to send Jurgen Klopp's much-changed Reds through to a last-four clash with Arsenal, which beat Sunderland 5-1 on Wednesday (AEDT) to seal its place in the semi-final.
A Vardy brace had initially put the Foxes 2-0 up early on at Anfield, and although Alex Oxlade-Chamberlain got Liverpool on the scoreboard, a spectacular James Maddison strike had Leicester cruising at the break. Vardy then hit the inside of Kelleher's right post on a breakaway which would have sealed his hat-trick and also extended Leicester's lead to three.
But half-time substitute Jota reduced the deficit back to one after the hour and Takumi Minamino equalised deep into stoppage-time to force a shootout after Liverpool, attacking the Kop end of Anfield, spent the majority of the second period putting the visitors under pressure.
Minamino was the sole Reds player to miss his penalty kick, but it mattered not as Kelleher denied Luke Thomas and Ryan Bertrand to allow Jota to wrap things up, Liverpool winning the shootout 5-4.