In the city where Christian Eriksen made his name, it was Dolberg –- another former Ajax player –- who opened the scoring with a fizzing strike in the 27th minute.
That came after Wales had started so well but Denmark never looked back and Dolberg struck again just after the restart before Joakim Maehle and Martin Braithwaite added more goals late on.
Carried by a wave of emotion, Danish dreams are still intact in a tournament that began in such traumatic circumstances for them with Eriksen’s collapse in their opening match against Finland in Copenhagen.
They now go on to a last-eight tie in Baku against the Netherlands or the Czech Republic.
Eriksen, still recovering at home after his cardiac arrest, was present in everyone’s minds at the home of Ajax, and that combined with a vast Danish support inside the one-third full Johan Cruyff Arena made this occasion really like a home game for them.
European champions against all odds when they beat Germany in the final on this day in 1992, Denmark finally have their first win in the knockout phase of a Euro since then and it would be a truly extraordinary story if they could repeat the feat this time.
Nobody in Denmark will want to get ahead of themselves but Wales — who finished with 10 men after Harry Wilson’s late red card — could certainly have no complaints about the outcome and there will be no repeat of their run to the semi-finals at Euro 2016.
They needed a moment of magic from captain Gareth Bale or Aaron Ramsey which never came, but in truth they were up against it from the outset.
Aside from the universal goodwill towards Denmark following Eriksen’s collapse, a ban on travellers from the United Kingdom entering the Netherlands meant there were very few Welsh supporters inside the stadium.
Danes, in contrast, descended in their droves on Amsterdam, creating an atmosphere not far off that seen at the Parken Stadium in Copenhagen when they beat Russia to qualify for the last 16 — even the Danish Prime Minister, Mette Frederiksen, was in attendance.
To their credit Wales started well, with the probing Bale leading by example in the early stages.
He crashed a shot just wide in the 10th minute, but then Chelsea’s Andreas Christensen –- Denmark’s third centre-back –- stepped up into midfield and they took control.
They were rewarded when Dolberg, now of Nice in France and selected ahead of Yussuf Poulsen in attack, collected the ball just outside the area and unleased a superb strike into the far corner of the net.
For Wales, the signs that it was not to be their night kept coming, as right-back Connor Roberts suffered a groin injury and had to come off.
Then giant striker Kieffer Moore was booked for a foul on Danish captain Simon Kjaer, meaning a suspension for the next round if Wales made it through.
Robert Page’s side would not make it through as they fell further behind three minutes into the second half.
Neco Williams, the Liverpool full-back who had replaced Roberts, tried to clear a Braithwaite cross but only succeeded in playing the ball straight to Dolberg who seized the chance to make it 2-0.
Bale and his teammates felt there had been a foul on Moore at the start of the move but the German referee waved away the complaints and the only surprise was that it took until the dying minutes for more goals to come.
Mathias Jensen picked out the unmarked Maehle to score the third in the 88th minute, before Wilson saw red for a foul on Maehle and Braithwaite made it 4-0, a goal given after a lengthy VAR review.
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