The result left a sizeable dent in the Dutch's chances of qualifying for the knockout phase from Group B but left Denmark well placed to reach the last eight for only the second time since their fairytale triumph at EURO 92.
Krohn-Delhi, 29, claimed the game's only goal in the 24th minute when he collected Simon Poulsen's deflected cross, swerved inside John Heitinga, and drilled the ball beneath goalkeeper Maarten Stekelenburg.
He was to test Stekelenburg on two further occasions and his industrious probing from the left flank saw him awarded the man-of-the-match award.
It was a particularly sweet evening for Krohn-Dehli, who joined Brondby from Ajax in 2008 after a two-year spell at the Dutch giants during which he was unable to make an impact, largely due to injury.
He also missed out on a place in Olsen's squad for the 2010 FIFA World Cup™ and the long-serving Danish coach, the only man to have amassed over 100 caps as both player and manager, admitted he should have taken him to South Africa.
"I made a mistake," he said in his post-match press conference. "Michael had an unlucky situation in Holland. He went to Ajax and was unlucky with injuries.
"Now he's at a good age, the best football age and he also played fantastically in the qualifying games against Norway and Portugal in the autumn. He was one of our best players in qualification, he's at the best age for a footballer, and I hope he can play many more years for the national team."
Olsen also reserved praise for Evian goalkeeper Andersen, promoted to the role of first-choice goalkeeper after Thomas Sorensen was ruled out of the tournament with a back injury sustained in a friendly against Brazil.
The 30-year-old made several key saves at Metalist Stadium, notably denying Robin van Persie from close range in the first half and throwing himself at the feet of substitute Klaas-Jan Huntelaar towards the end of the second period.
"Stephan was also very good," said Olsen. "Not just with his hands, but also with his feet. It was very important because he could start the play from the back. The Dutch team had some problems with that because they like to be the dominant team.
"He made a little mistake when the Dutch team hit the post (after Arjen Robben intercepted his misplaced pass in the 36th minute) but he continued in the same way and that was very important."
Denmark will now prepare to face Portugal on Wednesday, having already overcome Paulo Bento's side in qualifying, when a 2-1 win in Copenhagen in their final match condemned the 2004 finalists to the play-offs.