Both teams play in Baku for a chance to face either England or Ukraine in the semi-finals.
It took Denmark no time to take the lead, with Thomas Delaney scoring after less than five minutes from a corner.
Mikkel Damsgaard had a chance to make it 2-0 when he found himself inside the box with only the goalie to beat, but his finish was insufficient, and the Czech defense cleared.
After a botched kick out from Kasper Schmeichel in the 22nd minute, the Czech Republic had an opportunity to equalize, but the Denmark goalkeeper redeemed himself with a good save to deny Tomá Hole.
Joakim Mhle's wonderful cross was knocked in by Kasper Dolberg three minutes before halftime, putting the Danes 2-0 ahead.
That was the game's final meaningful opening, and the Czech Republic's tournament is over, while the Danes go to the quarterfinals.
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