But South Africa, one of the surprise teams of the tournament, gave the Dutch some nervous moments, forcing goalkeeper Daphne van Domselaar into a string of saves to keep Thembi Kgatlana at bay.
Netherlands lost to the U.S. team in the World Cup final four years ago and look like contenders again after finishing above the Americans in Group E.
South Africa had already exceeded expectations by advancing to the knockout stage for the first time after its dramatic 3-2 win over Italy in its final group game.
But goals from Roord in the ninth minute and Beerensteyn in the 68th, after an error from keeper Kaylin Swart, ended its unlikely run.
Netherlands went close to taking the lead just before Roord’s goal when Esmee Brugts swung in a curling shot that Swart had to push over the bar. Roord struck from the resulting corner.
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Sherida Spitse’s cross was headed toward goal by Lieke Martens, which forced Swart into action again. But from her save, the ball looped in the air and Roord headed over the line from close range to score her fourth goal of the tournament.
Danielle van de Donk was close to extending the lead but was denied by the feet of Swart from inside the box, and Kgatlana tested Van Domselaar as South Africa showed its threat on the break.
Kgatlana came closer still when through on goal just before the halftime, but couldn’t find a way past Van Domselaar. South Africa ended the half the stronger as Kgatlana repeatedly burst beyond the Netherlands defense.
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Its response to going behind was even more impressive, considering it had to contend with injuries to Jermaine Seoposenwe and Bambanani Mbane in the first half.
Netherlands regained control after the restart and the Dutch thought they’d doubled their lead when Martens turned and converted in the 54th. But their celebrations were cut short when it was ruled out on VAR review for offside.
South Africa offered little threat as it struggled to get possession and Netherlands scored its second after an error from Swart. Beerensteyn’s weak shot should have been easily caught by Swart, but she allowed it to squirm out of her control and over the line.
Just as in the first half, Netherlands’ goal sparked a reaction from the South African players and Linda Motlhalo was denied when Van Domselaar pushed her low effort round the post.
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The only negative for Netherlands was a yellow card for Van de Donk, who will now miss the quarterfinal match against Spain.
