Liverpool are through to the League Cup last eight after beating Chelsea on penalties, while holders Manchester City edged out Brighton on spot-kicks after an incredible 2-2 draw.
Likewise, Liverpool and Chelsea drew 1-1 at Anfield after both teams netted penalties.
The opening goal for the game came in the 40th minute from Chelsea as Morgan Rogers made no mistake from the penalty spot after Ryan Gravenberch brought down Moises Caicedo.
But Liverpool drew level three minutes later as Cody Gakpo scored from the spot after Wesley Fofana was penalized for handball.
Neither team had won before the sudden-death penalty shootout that followed, which was full of excitement.
Valentin Barco hit the post for Chelsea while the chance to win for Liverpool in the form of Kostas Tsimikas went over the bar.
Chelsea keeper Mike Penders gave the Blues a lifeline, but Liverpool survived as Giorgi Mamardashvili kept out Emmanuel Emegha’s effort. Joe Gomez netted, and Fofana missed to see the Reds through to the quarter-finals.
The defeat marked Xabi Alonso’s third loss in as many visits to Anfield.
Manchester City also needed penalties after a 2-2 draw at home to Brighton.
Brighton took the lead through Malick Yalcouye in the 30th minute before Mateo Kovacic equalised with an impressive long-range strike five minutes after the interval.
Georginio Rutter just after the restart, but Vitor Reis turned the ball in at the far post after a free-kick from Rayan Cherki in the 72nd minute.
Kovacic fluffed his lines from the spot, but goalkeeper Geronimo Rulli was the hero with saves from Yasin Ayari and Lewis Dunk to take City through.
Elsewhere, Bournemouth kept up their fine run of form by beating Aston Villa 3-0. The Cherries scored through Amine Adli, Lewis Cook and Alvaro Rodriguez to make it five wins on the trot in all competitions.
Crystal Palace while Sunderland overcame Brentford 3-2 with Chemsdine Talbi, Tymur Tutierov and Malick Fofana all scoring.
Liverpool will meet Bournemouth in the quarter-finals, with Manchester City playing Bradford and Sunderland taking on Crystal Palace.
Third-tier Fleetwood, who won on penalties against Arsenal on Tuesday, will face either Newcastle or Everton in the final quarter-final.
