Diogo Jota and Cody Gakpo each scored two goals as Liverpool began their defence of the Carabao Cup by coming from behind to thrash West Ham at Anfield.
The visitors stunned the holders by taking the lead after a corner, Wataru Endo's attempted clearance striking team-mate Jarell Quansah and rolling over the line.
West Ham's lead lasted just four minutes as Federico Chiesa marked his first start for the Reds with an assist after the winger's acrobatic volley into the ground bounced up for Jota to head the equaliser.
Portugal forward Jota scored his second early in the second half with a low and composed finish in front of the Kop after a lovely pass by Curtis Jones.
That goal came moments after West Ham had appeals for a penalty waved away when the ball appeared to strike the arm of Joe Gomez inside the box - with no video assistant referee (VAR) system until the semi-finals.
West Ham have now lost four of their seven games under manager Julen Lopetegui, who said afterwards he injured himself during the tie while stamping on the ground in annoyance.
"I have one little injury in my calf," said the Spaniard.
On a frustrating night, Lopetegui was booked for arguing with the officials as decisions went against his side, while Max Kilman missed a golden chance to make 2-2 from six yards.
Soon afterwards substitute Mohamed Salah made it 3-1 after Lukasz Fabianski had kept out Alexis Mac Allister's attempt, before Edson Alvarez was sent off for a second booking.
Cody Gakpo added to West Ham's misery with the fourth and fifth goals late in the tie as the Hammers exited the competition at Liverpool's hands for the second successive season.
Liverpool will go to Brighton in the fourth round on the week beginning 28 October.
Happy night under Anfield lights for Slot
This was Liverpool's first game in the competition since defeating Chelsea in the final at Wembley in February.
And Arne Slot's first-midweek experience under the Anfield floodlights proved a happy one as the Dutchman secured his most handsome win since taking charge.
While Liverpool got stronger as the game went on, West Ham became weaker and Alvarez's red card - two minutes after Salah had made it 3-1 - extinguished any hope of a comeback.
Lopetegui was clearly unhappy with some of the decisions by the officials.
When Danny Ings had a goal ruled out in the 18th minute for offside, he signalled for the officials to check VAR - only to realise the system was not in operation at this stage of the competition.
It summed up a deeply frustrating night for West Ham, who visit Brentford on Saturday in the Premier League (15:00 BST) looking to avoid a third consecutive defeat.
In contrast, Liverpool have won six of their seven league and cup games under Slot.
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