They too are seeking to match their 1998 achievement when they reached the quarter-finals before being beaten by Brazil in what was their best World Cup showing.
Croatia goalkeeper Danijel Subasic made three saves in the penalty shootout.
First, Mathias Jørgensen turned home in the second minute after Croatia failed to clear a long throw-in from Jonas Knudsen, the defender's shot creeping under Subasic to give Denmark the ideal start.
From there, the match petered out, with Denmark nullifying Croatia in the second half.
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This is the World Cup!
Zlatko Dalic's side will undoubtedly dominate possession in Nizhny Novgorod, and Denmark's defence will have to be well organised to keep Croatia out.
Croatia will once again depend on Modric, who has been in outstanding form, and fellow midfielder Ivan Rakitic to deliver the goods. The Scandinavian side are expected to stick around with Martin Brathwaite ahead of Yussuf Poulsen. It has been a long wait for both these sides to enter the knockout phase with Denmark last qualifying from their group in 2002 while Croatia did the same last in 1998. If Croatia's golden generation are to take this golden opportunity, they must improve on this.
Danish star Christian Eriksen believes his team can defeat Croatia within the regulation 90 minutes. I am sure they will create some chances, but most of their build-up play is under the "hopeful" category, unless they can get Christian Eriksen on the ball.
31 minute: Corner for Denmark.
Umtiti reveals difference between Messi at Barcelona, Argentina
We don't trust Argentina to shut out France , nor do we expect Les Bleus to deny the South Americans the goals they covet dearly. Messi scored against Nigeria in Argentina's final group stage match, helping boost the nation into the knockout stage.
Forwards: Mario Mandzukic (Juventus/ITA), Ivan Perisic (Inter Milan/ITA), Nikola Kalinic (AC Milan/ITA), Andrej Kramaric (Hoffenheim/GER), Marko Pjaca (Schalke/GER), Ante Rebic (Eintracht/GER).
Stay tuned here for live updates and highlights of goals and key plays from throughout the match (refresh here for most recent updates).
Denmark coach Age Hareide acknowledged that his players are writing their names in the history of their national team at the 2018 FIFA World Cup, but said they are focused on advancing as far as possible.
The Tottenham playmakers past and present hold down important roles for their national sides, with Modric outstanding for Croatia so far at Russian Federation 2018 and Eriksen Denmark's main attacking threat.
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It doesn't necessarily guarantee that he is staying with the Cavs, but I think it's a really good sign that he will. Far from it - he will be one of many top-flight picks that simply need time to develop over the next several years.