Croatia topped their group, winning all three of their group games.
Croatia's Luka Modric took the penalty saved by Danish goalkeeper Kasper Schmeichel who correctly dived left, holding the score at 1-1 as it would remain until the end of injury time.
The explosive start - both sides hit the back of the net within three minutes and thirty-seven seconds - was officially the quickest two teams have ever scored in a World Cup finals match.
Croatia players run toward goalkeeper Danijel Subasic (not pictured) after the penalty shootout against Denmark.
"I was nine years old".
65' - Croatia gets a chance with a well-placed corner, but the Denmark defense holds strong and clears the ball. "The fact they have gone 18 games unbeaten speaks volumes", he said.
"We have many good players, but we have a team which is what has taken us so far". His fellow defenders are expected to be Domagoj Vida, Sime Vrsaljko, Ivan Strinic - all were rested during the game against Iceland.
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Germany out of World Cup 2018
Low and his players will return to Germany on Thursday, but with the coach dismissing suggestions that dark times could lie ahead. Following their match against Sweden , Mexico's faithful turned their attention to the end of South Korea's game in Kazan.
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Croatia v Denmark TV Channel: How do I watch Croatia v Denmark on TV?
Modric scored a peach of a goal from distance against Argentina and along with FC Barcelona's Rakitic, has been pulling the strings brilliantly for his national team. 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.
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).
It didn't take long for the Croats to equalise, though, as Mario Mandžukić drew his side level nearly immediately after the restart to net from close range and against the run of play, 1-1.
Croatia beat Denmark in a dramatic penalty shootout on Sunday to progress to the World Cup quarter-finals.
Luka Modric admits he faces a "world-class" adversary in Christian Eriksen on Sunday but says it is time for Croatia's so-called "golden generation" to prove its quality.
"We're not going to lose 0-5 by trying to play tiki-taka football". But we stopped Lionel Messi in the game against Argentina, so we can do it again. The center-back pairing of Andreas Christensen and Simon Kjaer look like a ideal combination of youth and experience, while the team around them are physically strong and well-organized. In goal is Leicester City star Kasper Schmeichel.