Robin van Persie's second-half strike made Germany sweat in sweltering conditions, but Mario Gomez's two stylish first-half goals were eventually enough for Joachim Löw's side to move to the brink of the last eight and leave the Netherlands staring down the barrel.
The Metalist Stadium in Kharkiv was the venue, but this was a victory made in Munich. Those who doubted Germany's FC Bayern München players' powers of recovery after last month's UEFA Champions League final defeat were silenced in emphatic fashion.
Bastian Schweinsteiger supplied two fine assists and club colleague Gomez a pair of exquisite finishes. Van Persie halved the Oranje's arrears but it was not enough and the Dutch stay bottom of Group B without a point. They could yet become the first team ever to qualify from a EURO section with three points, but the odds look to be stacked against them. For Germany, the quarter-finals are in sight thanks to their 13th successive competitive triumph.
Germany had beaten the Dutch 3-0 in a Hamburg friendly last year; this was the real thing and they inflicted further punishment once some early scares were behind them. Van Persie twice might have put the Dutch ahead inside 11 minutes but he could only stab a long pass straight at Manuel Neuer before dragging wide having latched on to Arjen Robben's through ball.
Germany are a team so well choreographed that there never looked to be too much doubt they would come good. Mesut Özil was the star of their first act, unleashing a fierce volley against a post, but there were two men waiting in the wings ready to orchestrate proceedings.
Though Schweinsteiger was conductor and director rolled into one, there was no doubting the protagonist. There were 24 minutes on the clock when Bayern's No7 turned it on for the first time, threading the ball through the eye of a needle for Gomez, who made space with a balletic pirouette before finishing with a flourish; top marks all round.
Holger Badstuber fluffed his lines when his point-blank header struck Maarten Stekelenberg, but only a minute later it was 2-0. The man they call 'Schweiny' caressed a delightful first-time pass down the inside-right channel and Gomez flashed a shot over Stekelenberg without breaking stride. Stekelenberg then kept the Netherlands in the game when he tipped over Özil's deflected free-kick, but Van Marwijk was in need of his supporting cast; Klaas-Jan Huntelaar and Rafael van der Vaart were inevitable half-time changes.
Though the unlikely figure of Mats Hummels nearly rendered those changes meaningless soon after the interval, Stekelenberg twice stayed big. The Dutch then came back, with Van Persie's snapshot kept out by Neuer's smart stop low to his right.
That was merely the latest flash of frustration for the Dutch. Tense before the game, they were now positively tetchy – Robben rushed when free in the area and Sneijder shot straight at Jérôme Boateng, but Van Persie clearly had not read the script. In a flash, the Arsenal FC man duly reminded us why he scored 30 league goals this term, receiving the ball wide on the right with his back to goal before cutting inside and letting fly with a rasping drive from outside the penalty area.
It was as good as it got for the Dutch, however, and though the fat lady is yet to sing, the curtain is nearly down.