The unlikely architect of Friday night's victory was veteran defender Andy Robertson.
The Scotland captain broke the deadlock with his first goal since September and then crossed for Mohamed Salah to score on this ground for the second time in four days, all within the space of three second-half minutes.
Curtis Jones extinguished the hosts' hopes by curling home a low shot from the edge of the area as the 2022 winners cruised into the quarter-finals for only the fourth time since reaching the final in 2012.
After Tuesday's dreadful Premier League defeat at the same venue, the visitors - and Slot in particular - could not afford any more damage and were deserved winners.
Seventeen-year-old winger Rio Ngumoha made the most of a rare start with a man-of-the-match performance ahead of Robertson, but it was the veteran left-back who produced the game-changing moments.
The defender, who next week turns 32, proved he still has plenty to offer the team but with the status of his expiring contract remaining unresolved there may be a dwindling number of opportunities for him to contribute having been relegated to second-choice by Milos Kerkez.
Ngumoha would benefit hugely from having such experience behind him as he continues his rapid development but, with Liverpool potentially looking at options for the left wing, that may be of less importance to the Reds hierarchy.
The youngster departed in the 69th minute - replaced by summer signing Florian Wirtz who was back from injury - having been a constant problem for Wolves' right-sided wing-back Jackson Tchatchoua.
Ngumoha, making only his fifth start, utilised his pace and for the majority of the half it was he and not Salah who saw the most ball.
In the second half, Ngumoha picked up a loose ball deep in his own half and it was moved left to right through Cody Gakpo and Salah before coming back to the left where Robertson had joined the attack and he let fly from 20 yards to beat Sam Johnstone.
His low cross into the six-yard box was then rifled into the roof of the net by Salah, who was left bewildered by an offside flag but not for long as, at this stage of the competition VAR is in operation, he was ruled to have been behind the ball.
Fittingly Robertson finished the match wearing the armband after Virgil van Dijk was given a well-deserved rest but not before Jones had banished the frustrations of Tuesday with a strong run and finish.
Hee Chan Hwang then snatched an added-time consolation for the hosts.
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