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Virgil van Dijk made a dream start for Liverpool following his £75m move from Southampton as his late header settled a highly competitive FA Cup third round Merseyside derby against Everton at Anfield.

The visitors looked on course for a replay at Goodison Park until keeper Jordan Pickford misjudged a corner allowing Van Dijk, who cost a world record fee for a defender, to steal in six minutes from time and send the Reds into the fourth round.

Gylfi Sigurdsson’s smooth finish from the edge of the area put Everton level in the second half after Liverpool had taken the lead 10 minutes before half-time, with James Milner scoring from the penalty spot following Mason Holgate’s tangle with Adam Lallana.

In a fiercely fought game there was a first-half flashpoint when Holgate foolishly pushed Reds forward Roberto Firmino over the advertising hoardings and into the crowd, with the Everton defender left furious after the pair subsequently exchanged words.

Liverpool were without injured forward Mohamed Salah and midfielder Philippe Coutinho, who has been linked with a £140m move to Barcelona.

Liverpool manager Jurgen Klopp wasted no time in introducing Van Dijk to his defence after he finally made his move from Southampton – but it was in attack where the 26-year-old Netherlands international fulfilled his dreams in front of the Kop.

He had already wasted one chance to mark his debut with a goal when he could only head at Pickford from six yards. He made no mistake when presented with that crucial opportunity six minutes from time.

Van Dijk got to the ball ahead of Pickford, whose rash attempt to claim was heavily punished as Anfield went into ecstasy.

It is in defence where he will be expected to do his main work, but this was a highly impressive debut at both ends for the Dutchman.

Van Dijk cuts an imposing figure and was almost unbeatable in the air up against the game and tireless Dominic Calvert-Lewin.

Greater tests than this lie ahead. Everton boss Sam Allardyce was unable to use the threat he hopes will come with the £27m arrival of Turkey striker Cenk Tosun, so Everton’s danger was limited.

As a starter, though, this was exactly what Klopp and Liverpool had in mind when they handed over £75m to Saints.

Merseyside derbies can always prove difficult occasions for referees – and this was no different as Bobby Madley had to deal with several contentious incidents.

Madley booked Wayne Rooney as early as the seventh minute for a reckless challenge on Joe Gomez – and he needed to keep an eye on the boyhood Evertonian as he sailed very close to the wind, and a second yellow card, before being substituted after 52 minutes.

He was in the action again on 35 minutes when he pointed to the spot after Holgate tangled with Lallana. Everton will complain it was a soft award – as Liverpool did when Dejan Lovren was punished with a penalty when he manhandled Calvert-Lewin in the recent 1-1 draw at Anfield – but once the Toffees defender laid hands on his opponent he was asking for trouble.

The biggest flashpoint came moments later when Holgate had a rush of blood to the head and shoved Firmino into the crowd. The incident boiled over as the Brazilian rushed back at Holgate to protest – angry words were exchanged and Everton’s youngster reacted with undisguised fury to something Firmino said.

After that, Madley was able to keep a check on the emotions as a game that was passionate never threatened to get out of hand.

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