Liverpool required two pieces of brilliance from striker Luis Suarez to bypass Stoke City and reach the last eight of the League Cup, a competition the club have won seven times.
Kenwyne Jones had taken advantage of Sebastian Coastes’ error to put the home side in front, but Suarez’s wonderful individual effort leveled the scores.
And with five minutes remaining, the Uruguayan headed in Jordan Henderson’s deep cross to send The Reds through.
Manchester City continued their scoring spree in beating Wolverhampton Wanderers at Molineux.
Nenad Milijas opened the scoring mid-way through the first half, but the opener worked to inspire City to another destructive performance.
After Adam Johnson had swept home the equalizer, the England winger set Samir Nasri free to help give City the lead.
Edin Dzeko then tapped in twice either side of Luca Scapuzzi’s first goal for the club on his first start.
Substitute Jamie O’Hara rounded off the scoring with his first touch for a spirited Wolves side.