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.
It was a fine finish to a game that was otherwise low on quality, as Liverpool, clearly worn out from their Christmas travails, sank to the level of a tiresome Sam Allardyce Blues side, gifting a sloppy equalizer to Gylfi Sigurdsson after a first half penalty from James Milner had put Jurgen Klopp's team ahead. Even in the white heat of a Merseyside derby - and a knockout, winner-takes-all one, at that - the world's most expensive defender managed to attract attention.
Liverpool manager Jurgen Klopp handed a debut to record £75 million ($102 million, 85 million euros) signing Van Dijk as he selected arguably his strongest available starting line-up, in contrast to the 1-1 draw in the Premier League played out by the sides in December.
The atmosphere in the stands crackled and on the pitch it was equally feisty.
Chances, though, were at premium in the first half as Liverpool dominated possession. "The first one was no penalty in my opinion and this one wasn't also", Klopp said. "It's the same. There is contact and the referee used his whistle". Gylfi Sigurdsson equalized in the 67th but Everton's winless run at the home of its great rival extended to 21 games, dating back to 1999. "Exactly the same situation". His anticipation an reading of the game always saw that he was in the right area to cut out Everton's attacks, and at the very least, cut down the angles enough to prevent them from getting shots off - he was hardly at fault for Sigurdsson's goal as the majority of Liverpool's players were caught too far up field after Everton had won possession following a corner kick.
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.