Kenneth Zohore's ball in the box found the Grasshopper Zurich winger, who turned inside the area with his first touch before firing home past Lucas Zima.
A further seven minutes would elapse before Denmark were in front once more, Mads Pedersen's cross from the left finding Zohore, who poked the ball home into the bottom right corner.
Tomas Chory would pull his side back into contention early in the second half as he powered in a header from close range at the back post from a Jakub Jankto cross.
However, the Danes took the lead once again in the 73rd minute through Zohore and would not relinquish it this time, with Marcus Ingvartsen killing the game off late in the second half.
The Czechs, who harboured hopes of topping the group prior to their final Group C game, go home bottom of the pile with three points from three games.
Denmark, meanwhile, finish third on the same number of points but a better goal difference, ending the group stage on a high after losing their first two matches.