The unfancied East Europeans, who lost 1-0 to England in the group stage, now march on to Azerbaijan where they face Denmark in the quarter finals on Saturday.
While they were under the cosh for much of the first half and were lucky to escape going behind several times in the second, the sending off of Matthijs de Ligt proved decisive.
Defender Tomas Holes and striker Patrick Schick followed up with two goals in 12 minutes that ended Holland’s recent revival in major tournaments after an enthralling contest.
The knockout stage puts the fear of God into some teams, makes others cautious and cagey, while for some it lights a firecracker in their boots.
The Dutch, resplendent in their traditional all-orange backed by banks of noisy and colourful travelling fans, were at it from the off.
The tempo was similar to that in the first Group C game exactly a week previous against Ukraine, with a buzz to the game and Holland dominant.
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It was surprising it took Frank de Boer’s team until the second half to score their first goal but at least the football skipped along.
A stark contrast to so many England games where they draw the sting out of the opposition but also drain much of the entertainment value out of the occasion in doing so.
The Czechs managed a couple of probing runs into the opposition half but it was mainly wave after wave of brightly-attired men sweeping forwards in Holland’s enterprising front line.
Included in that is improving rookie Donyell Malen, the PSV Eindhoven striker who kept his place in the starting line up from the last group game.
Malen’s youthful engine and composure on the ball led to an outstanding goal as the Dutch signed off the group stage with an exhibition match against North Macedonia to maintain their 100 percent record.
Combining with Memphis Depay and with stand-in skipper Georginio Wijnaldum supporting from midfield, Holland were unlucky not to go ahead in the eighth minute.
There was a suspicion of offside when Matthijs de Ligt headed Daley Blind’s diagonal ball into the box back across goal from the far post with Wijnaldum following up to slash a shot wide.
Without seriously troubling Tomas Vaclik in the Czech goal, a Holland team which has been lambasted for being too negative chased every ball, pressed high and treated us to the kind of high-speed football uptight England rarely offer up at the moment.
The under-pressure Czechs mustered only two serious chances in the first half.
The first of those was a diving header from West Ham midfielder Soucek, skipper in place of injured Vladimir Darida, at the near post.
Antonin Barak missed the best when put through on the edge of the six yard box but he was too slow to pull the trigger and his shot took a slight deflection to fire wide.
But if the first half was steadily entertaining, the drama really took off after the break.
Vaclik’s nerveless disposition kept his team level in the 52nd minute when Malen broke free from midfield by squeezing through the inch-wide gap between defenders Tomas Kalas and Pavel Kadarabek.
But the looming presence of Vaclik standing firm in front of his goal was enough to put the inexperienced one-time Arsenal player off and the brave keeper dived at the striker’s feet to grab the ball.
Barely a minute later Holland’s superiority was undermined when centre half Matthijs de Ligt was sent off for deliberate handball following a length VAR check of which English ref Stuart Attwell was at the controls yesterday.
Juventus centre half de Ligt was initially given a yellow by the Russian ref on the pitch but after consulting his pitchside screen it was upgraded to red leaving Holland down to ten men for the last 35 minutes of a winner-takes-all game.
The breakthrough arrived as the Dutch wobbled with the momentum against them in the 68th minute.
A free kick taken virtually from the corner flag swung into the area where Bristol City defender Tomas Kalas was at the far post there to head it straight back across the six yard box.
The weakened Dutch defence had taken their eyes off wingback Tomas Holes who was left unattended to powerfully nod the ball over the line despite three men in orange on the line to protect the goal.
With Holland now chasing the game Schick nailed it with ten minutes to go when he collected a square ball into the box and fired low to Stekelenburg’s right for number two.
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