A sledgehammer to crack a nut was the expression that came to mind as Liverpool’s new £75m defender made his debut against a side with only one goal in their last four games and no shots on target in either of their last two home matches. Everton supporters were clinging to the slender hope that Jürgen Klopp might have taken a risk in throwing Virgil van Dijk straight into the heat of a Merseyside derby.

There were few worries on that score, even before the centre-half scored the winning goal five minutes from the end. Joël Matip and Van Dijk had only Dominic Calvert-Lewin to look after between them and the latter towered over the Everton centre-forward in every sense, invariably getting to the ball first whether in the air or on the ground. The former Southampton player even found time to launch a few attacks in the first half, sometimes carrying the ball to the halfway line, sometimes sending out 50-yard passes in search of team-mates further forward.

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Van Dijk looks the part, in short, but then he always did. It was in the other half of the pitch that Liverpool looked unusually disjointed until Everton came to their aid with a couple of defensive blunders. First was a penalty as soft as the one that earned them a point in the league derby at Anfield last month. With only two of the Fab Four on the pitch Liverpool were making hard work of breaking through Everton’s two banks of defenders before Mason Holgate made his first misjudgment of the evening.

The defender made the error of laying his hands on Adam Lallana as the Liverpool forward attempted to turn on the ball just inside the area. There was no question of throwing him to the floor or ripping the shirt from his back but Lallana felt the contact and went to ground anyway. It was almost an exact replica of the challenge Dejan Lovren made on Calvert-Lewin for the penalty in the league game, and as Sam Allardyce fully backed that decision he could have no complaints here. “Don’t raise your hands, don’t touch the opponent, don’t mess with him” was the gist of Allardyce’s advice last month, so he probably needs to have a word with Holgate about keeping his hands to himself to avoid undoing half an hour’s worth of otherwise doughty defending.

Allardyce would have been reasonably pleased with that first half- hour too, because not only had Everton been keeping Liverpool at bay; they had won two corners to the home side’s none. There were no shots on target, needless to say, but as far as Allardyce is concerned corners are the next best thing. Everton must have been hoping to make it to the interval without conceding, to at least raise the tension levels, though in the event they were lucky to make it to half-time with a full complement of players on the pitch.

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At first sight it seemed ludicrous that Holgate should make his second misjudgment of the evening by deliberately shoving Roberto Firmino over the perimeter fence into the crowd and get away with it, though the Everton player lost his head to such an extent that it appeared likely he had been verbally abused or provoked. There was no other explanation for such a blatant transgression under the nose of the referee, and the fact that Robert Madley failed to produce a card – not to mention the amount of time he spent talking to the fourth official and discussing the matter behind his hand with various interested parties on the pitch – suggested this was a complex incident that even VAR might not have been able to clear up. Whatever the provocation, Holgate was lucky to get away with using his hands again so soon after conceding the penalty.

With Everton chasing the game in the second half Allardyce permitted Liverpool supporters their biggest cheer of the night by withdrawing Wayne Rooney well before the hour mark. Ademola Lookman was sent on in his place, but it is debatable whether Allardyce was trying to boost his attack. More likely he was protecting Rooney, who had picked up an early booking for a foul on Joe Gomez and had looked in danger of collecting a second when he clattered into Emre Can.

Nevertheless Lookman played his part in helping set up an unlikely equaliser, moving the ball neatly upfield to find Phil Jagielka, of all people, hovering close to the Liverpool penalty area, ready to lay off to Gylfi Sigurdsson. One shot on target, one goal. Set up by a substitute and a centre-half it may have been, but for just a few minutes it appeared Everton under Allardyce might have a charmed life in Merseyside derbies, especially after Lallana and Gomez wasted good chances to put the game to bed. Any Allardyce team has to be able to defend corners, however, and Everton were ultimately undone by a lapse of concentration almost as big as a £75m Dutchman.