Morocco edged past the Dutch 3-2 on penalties to set up a last-16 showdown with Canada on Saturday, with Ismael Saibari claiming the decisive goal after Yassine Bounou saved Crysencio Summerville's penalty and multiple missed opportunities and saves on both sides.
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It came after Cody Gakpo had given Netherlands the lead in the 72nd minute following a superb break from Summerville. What followed were emotional scenes as Gakpo wiped away the tears, days after the 27-year-old and his partner Noa van der Bij announced they had experienced the loss of their unborn son.
Momentum had shifted again and it looked likely Gakpo's goal would be the decisive one, but a cross in the 90th minute found a charging Issa Diop, whose header found the corner of the goal and ensured the match would go into extra time.
Morocco created the best chance of the extra 30 minutes and looked certain to take the lead when Soufiane Rahimi was one-on-one with Bart Verbruggen, but the Dutch goalkeeper was somehow able to deflect the shot from point-blank range in what was the save of the tournament so far.
However, he could not repeat the heroics in the shoot-out as Netherlands became the second European side to be heading home on penalties in a matter of hours after Germany's shock penalty defeat to Paraguay.
The key moments from Monterrey...
72: GOAL! Gakpo broke the deadlock, sparking emotional celebrations from Netherlands.
90+1: GOAL! Diop grabbed a dramatic equaliser as Morocco sent the tie to extra time.
96: SAVE! Verbruggen produced the save of the tournament to deny Rahimi from point-blank range.
PENALTIES! Shoot-out drama as Netherlands missed three penalties and Morocco missed two.
PENALTIES! Saibari eventually scored the winning penalty as Morocco set up a last-16 clash with Canada.
Koeman tactics backfire as Netherlands' World Cup wait goes on
Sky Sports' Oliver Yew:
"Ronald Koeman is going to have questions to answer as Netherlands failed to reach the last 16 for a World Cup they have competed in for the first time since 2006.
"His side had looked a real threat in the group stages, scoring 10 goals, including a 5-1 win over Sweden.
"However, a switch to a back five against Morocco saw them surrender possession as the African side dominated the game.
"Gakpo's goal and Verbruggen's heroics almost got the Dutch out of trouble but in the end, Koeman's set-up and his defensive changes eventually saw them come unstuck.
"Koeman's tactics will now surely come into question as Netherlands' disappointing exit is analysed. The negative set-up completely backfired as Netherlands' agonising wait for World Cup glory goes on."
'Netherlands win big for Morocco'
Morocco defender Noussair Mazraoui said:
"A really tough game against a really tough opponent. One of the best opponents you can face in the world. It's a top 10 in the world, I think a contender to eventually win the World Cup.
"The way that we managed to win today is a huge acknowledgement for us as a national team."