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Liverpool manager Juergen Klopp celebrates with Virgil van Dijk at the end of the FA Cup third round clash against Everton at Anfield on Friday. Image Credit: Reuters

Liverpool: It couldn’t have gone any better for Virgil van Dijk on his Liverpool debut.

Signed last week for $100 million as the world’s most expensive defender, Van Dijk scored an 84th-minute winner against Everton — Liverpool’s fierce local rival — in front of the storied Kop stand at Anfield in the third round of the FA Cup on Friday.

“Playing at Anfield for Liverpool is a dream for every player,” the Netherlands defender said after the 2-1 win in the 230th Merseyside derby. “To score a goal is even more special.”

Manchester United also left it late to qualify for the fourth round, with in-form midfielder Jesse Lingard and striker Romelu Lukaku scoring in the final six minutes of regulation time in a 2-0 victory over second-tier Derby County at Old Trafford.

Dream debut

Kevin Keegan, Michael Owen, Luis Suarez and Mohamed Salah are among those to have scored on their Liverpool debuts.

Add Virgil van Dijk to the list.

Liverpool manager Juergen Klopp said the centre back wasn’t “fine-tuned” following his big-money move from Southampton and he wasn’t even going to start him until the morning of the match, when he changed his mind.

Van Dijk looked a bit rusty with the ball at his feet but was commanding in the air throughout, no more so than when he leapt in front of Everton goalkeeper Jordan Pickford at a corner to head the ball into an empty net.

“I think something like that is quite special,” Klopp said.

James Milner put Liverpool ahead in the 35th minute by converting a penalty, contentiously awarded after Adam Lallana fell to the ground after Mason Holgate placed his hands on the chest of the Liverpool midfielder.

Everton barely threatened in the first half but was much more dangerous after the break, equalising through Gylfi Sigurdsson after a counterattack following a Liverpool corner.

The most explosive incident in a typically high-octane derby came just after Milner’s goal when Holgate shoved Roberto Firmino into — and over — the advertising boards. A clearly unhappy Firmino vaulted back onto the field and sprinted toward Holgate, swearing in Portuguese, and was lucky that referee Bobby Madley stepped in between them to intervene.

Holgate then became aggrieved, and appeared to complain to Madley that he had been verbally abused by Firmino. Madley spoke to his the fourth official, before play continued.

Liverpool hasn’t lost to Everton in 16 matches — a club record — and Everton’s winless run at the home of its great rival extended to 21 games, dating back to 1999.

Late show

Jesse Lingard’s latest scintillating strike for Man United came as Jose Mourinho’s team looked set to be taken to a replay.

In the 84th minute, Lingard teed himself up and smashed home a swerving volley for his eighth goal in 10 games. He spent time on loan at Derby in 2015.

Lukaku added a second in the 90th minute when he controlled Paul Pogba’s long clearance on his chest in midfield, played a one-two with Anthony Martial and scored with a powerful strike.

A quarter final exit in the League Cup and a 15-point deficit to leader Manchester City in the Premier League has placed extra importance on the FA Cup for United, which fielded a strong line-up.