New goalkeeper Alisson started for Liverpool, before Loris Karius was given a rousing reception when he replaced the Brazilian in the second half, just over two months after suffering concussion and making two terrible errors in the Champions League final defeat by Real Madrid.
In the second half at Anfield, midfielders Fabinho - who missed an early penalty - and Marko Grujic both filled in as Van Dijk only played 45 minutes, but Klopp is not anxious ahead of Sunday's visit of West Ham.
In the biggest moment of his young career, two incredible errors from Karius proved to be the difference between the Reds and Real Madrid, with the goalkeeper tearfully apologising to traveling Liverpool fans after the final whistle.
He was clearly moved by this emotional gesture on the pitch and tweeted afterwards: "Thank you Anfield for this reception!".
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Liverpool manager Jurgen Klopp then made seven changes at the break with Xherdan Shaqiri, Andy Robertson, Marko Grujic, Curtis Jones, Adam Lallana, Daniel Sturridge and Danny Ings all making an appearance with Shaqiri providing the assist on the final goal.
Liverpool's title bid does not just depend on how they fare.
"I was not surprised, to be honest, but as a human being I was hoping for it and I loved it", he added. Is it possible being different in a really hard world? "We showed a really nice face, and that helps not only Loris but the others as well, that they see this is a very special place".
This lead to Karius being the subject of a wave of abuse on social media, some of it going way past the typical football jokes you would see after the games, with death threats amongst several vicious messages targeted at the German goalkeeper.