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They are the first side to qualify for next year’s tournament other than the hosts, who qualified automatically.
It leaves them safely through from UEFA qualifying Group J with an eight-point lead over Romania with two games to play.
Elsewhere in European qualifying action, Wales took a vital step forward as they look to secure second in Group E with a nervy 1-0 win over Estonia in Tallinn.
Kiefer Moore’s early goal proved the difference between the two sides as the hosts squandered a couple of chances to draw level.
It leaves Wales’ fate in their own hands, level on points with the Czech Republic but with a game in hand, with Belgium likely to top of the group.
However striker Moore will now miss Wales’ next game against Belarus after the referee deemed a raised arm to be worthy of a yellow card as he jostled for position in the box.
“It is disappointing - I want to play every game,” Moore told Sky Sports after full-time.
— Wales 🏴 (@Cymru) October 11, 2021
“Today was all about grinding out a result and we did it at as a team. I think every time we come together it is always good. We epitomise that together, stronger, and it is in our hands now.”
The night’s big scoreline came in Amsterdam as the Netherlands thrashed Gibraltar 6-0.
Memphis Depay scored twice for a Dutch side that registered more than 30 attempts on goal.