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The £75m club-record signing marked his first game for the Reds with a bullet header.
Liverpool saw off their Merseyside rivals 2-1 at Anfield in the FA Cup third round tie last night.
And Van Dijk was not even expected to start yesterday.
The centre-half did not have much game time over the Christmas and New Year period due to his impending exit from Southampton.
But Klopp felt Van Dijk was sharp enough and ready to face Liverpool’s arch rivals.
Virgil van Dijk makes his Liverpool debut
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“A fairy tale in a world with not a lot of fairy tales anymore”
Jurgen Klopp
“A fairy tale in a world with not a lot of fairy tales anymore," Klopp said. “So I think something like that is quite special.
“It was a difficult decision to make to be honest because, to be 100 per cent honest, the first plan was not to start him tonight.
“But then Dejan [Lovren] and Raggy [Ragnar Klavan] played a lot of games in the last few weeks, so I changed my mind this morning. And it helped!
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"He showed a lot of things we want him to show in the future very often tonight; heading of course, football-wise his first touch was good, good under pressure and then around set pieces a proper threat."
Klopp’s late call to start the Dutchman paid off for Liverpool.
And Van Dijk can now look to play an important role in the Reds’ next game - a crunch showdown with Premier League leaders Manchester City.
Pep Guardiola’s men visit Anfield next Sunday (4pm).