Robin van Persie and Arjen Robben led Holland’s procession of misses either side of the Denmark striker’s 24th minute clincher.
Danish defender Daniel Agger saw his second-minute flick-header held by Maarten Stekelenburg before relaxed Dutch passing took almost total control.
Van Persie hooked wide from 12 yards and Robben cut inside for a low shot foiled by Stephan Andersen as classy Holland looked certain to break through.
But instead Krohn-Delhi’s fourth goal in six games defied the tide of play.
Simon Poulsen’s attempted cross ricocheted back for the Danish striker to snake into the left of the box and drill home through Stekelenburg’s legs.
Holland briefly reeled but soon resumed their domination of chances and possession.
Robben remained their liveliest first-half menace, initially down the right, then on the opposite flank.
And it was the Bayern Munich winger who dashed onto keeper Andersen’s poor pass-out, weaved into space and curved a left-footer off the post.
Ibrahim Afellay’s long-ranger teed him up for a long-ranger just wide as Denmark continued to defend in depth.
But the Danes stretched Holland a few times on the breal just before the interval, Krohn-Delhli conjuring a low drive well held by Stekelenburg.
Van Persie, though, should certainly have levelled on 43 minutes.
Wesley Sneijder slotted he ball across to the Premier League’s double player-of-the-year in ample space near the penalty spot. But Van Persie controlled horribly with his left foot and his hurried shot from his second touch was smothered by Andersen.
Holand upgraded their superiority to an urgent peppering of the Denmark goal straight after the interval.
Van Persie fumbled an inviting pass into the box from Robben, then saw Andersen thwart his sharp turn and snap-shot.
Sneijder grew in influence as Holland dictated play.
And a 25-yard stinger fellow midfielder Mark van Bommel provoked the save of the game from Andersen, a flying tip-round to his right.
Hitman Jan Huntelaar finallyu came on to address Holland’s string of misses.
And his impact was almost immediate.
Sneijder’s majestic long pass, with the outside of his right foot, left the substitute controlling deftly but seeing his 75th minute shot blocked by the onrushing Andersen. The Danish keeper was then rescued by referee Damir Skomina when van Persie challenged robustly for the rebound.
Denmark’s defending gained composure as Holland lost much of their momentum.
But still Robben busrt through tto angle a drive high and wide when he should have fed a striker.
Denmark survived storng penalty appeals and a late siege to seal one of their most famous victories ever
Netherlands: Stekelenburg, Van Der Wiel, Heitinga, Vlaar, Willems, Van Bommel, Nigel De Jong, Robben, Sneijder, Afellay, van Persie. Subs: Vorm, Mathijsen, Bouma, Kuyt, Huntelaar, Schaars, Strootman, Luuk De Jong, Narsingh, Boulahrouz, Van der Vaart, Krul.
Denmark: Andersen, Jacobsen, Kjaer, Agger, Simon Poulsen, Kvist Jorgensen, Zimling, Rommedahl, Eriksen, Krohn-Delhi, Bendtner. Subs: Lindegaard, Christian Poulsen, Bjelland, Okore, Schone, Silberbauer, Pedersen, Wass, Jakob Poulsen, Kahlenberg, Mikkelsen, Schmeichel.
Referee: Damir Skomina (Slovenia)