It was a victory that came courtesy of two dreadful errors from England in the extra period and thanks to the intervention of a VAR review that cancelled out what could have been a winner for Gareth Southgate's side in the 83rd minute.
But the specifics of the deciding goals -- after the game was level at 1-1 in 90 minutes -- should not take away from the achievement of Koeman's team in setting up a fascinating clash with Cristiano Ronaldo and company on Sunday in Porto.
A year on from a World Cup the Dutch watched from home having failed to qualify, their young side now have a chance of winning UEFA's new tournament and, whatever status that brings, Koeman cannot be anything but delighted with their progress.
To reach the last four in Portugal, the Netherlands had to finish top of a group with 2018 World Cup winners France and four-times world champions Germany -- beating both on home soil.
Then the Dutch had to come from behind on Thursday against an England team that reached the semi-finals in the last World Cup in Russia and came into this competition with a real sense that they could win their first major silverware since 1966.
While England will rue their defensive errors, the Netherlands certainly showed why they are going to be genuine contenders in next year's European Championship.
Although much of the buzz around the Dutch has focussed, rightly, on the young talent in an exciting Ajax Amsterdam team that reached the Champions League semi-finals this season, Koeman has been able to blend them with an experienced core.
Champions League winner Virgil van Dijk at the back is a once in a generation quality centre-half, while in midfield his Liverpool team mate Georginio Wijnaldum combines technical skill with a physical presence and football brain.
At left back Daley Blind delivered a composed and assured performance that must have left Manchester United fans wondering if their struggling club let him go too soon.
DE JONG'S QUALITY
But the player who stood out at a rainy Estadio Afonso Henriques, was the 22-year-old central midfielder Frenkie de Jong who will move from Ajax to Barcelona next month.
In a game with more than the amount of mistakes expected at this level, De Jong's consistent quality shone through.
In the bustle of midfield, his touch was light, his vision sharp and his delivery precise, while everything about his display suggested that this is a player ideally suited to continue the fine tradition of Dutch players at the Nou Camp.
De Jong controlled the tempo, bringing in the wide players and utilising the pace of Memphis Depay on the break, but also slowing things down and taking the sting out of England's spells of dominance.
At the back, Matthijs de Ligt recovered from the poor control which forced him to give away the penalty which Marcus Rashford converted to put England ahead in the 32nd minute.
He made amends with a thundering header from a corner in the 73rd which brought the Dutch level but he also showed as the game went on why most of Europe's top clubs want his services.
If there is a weakness in this Netherlands side it is in attack. Depay may have rebuilt his once floundering career since moving from Manchester United to Olympique Lyonnais but he would benefit from a bigger goal threat alongside him.
That absence of sharpness up front was compensated for by England's shocking defensive mistakes in extra time when a John Stones error resulted in Kyle Walker scoring an own goal and Ross Barkley gave the ball away to allow Quincy Promes to score.
The Dutch can expect fewer gifts from the hosts on Sunday.
The Netherlands have though brought style and class to the beautiful game since the 1970s and those who have appreciated their football across the decades can only be pleased to see them moving back to the upper echelons once again.
(Reporting by Simon Evans; editing by Ken Ferris)
