A typically crucial Divock Origi volley deep into stoppage time levelled the tie at 5-5 as the Reds twice came from two goals down to send the match to spot-kicks.
Young goalkeeper Caoimhin Kelleher denied Dani Ceballos with the only save of the shootout, and Academy graduate Curtis Jones fired home the winning penalty to give the Reds a 5-4 win.
Here are five talking points from an action-packed night at Anfield...
Jones dazzles in spotlight
On as a 55th-minute substitute with his team 4-2 down, teenage Scouser Jones finished the match as one of Liverpool's triumphant heroes having made a major impact on the tie.