Slovakia coach Vladimir Weiss could only reflect that his fears that, if the quicksilver winger played he would improve the Dutch by 50 percent, proved spot on.
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Robben, in his first start in South Africa after suffering a hamstring injury, served up a man-of-the-match display capped by the opening goal before exiting with 20 minutes to go with the match all but settled.
The victory extended the Dutch team's unbeaten run to 23 games and set up a quarter-final appearance in Port Elizabeth on Friday against the winners of Brazil against Chile, who play later on Monday.
Robben opened the scoring on 18 minutes, powering down the right after collecting a superb crossfield pass from Wesley Sneijder. He then jinked inside two defenders and drilled a low, left-footed shot past Jan Mucha.
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"That was nice today. If you're at the World Cup it should be fun. We didn't play our best match today, but the important thing is that we advanced," Robben said.
The second goal came with just six minutes to go. Captain Giovanni van Bronckhorst floated a pass to Dirk Kuyt on the edge of the penalty area, he headed past the stranded Mucha and crossed for Sneijder to side foot easily into an empty goal.
Slovakia's Robert Vittek slotted home a penalty in the fourth minute of injury time, making him Slovakia's record goalscorer with 23, but it was scant consolation after he fluffed two excellent chances to equalise.
LITTLE VENOM
After opening the scoring, the Dutch sat back for much of the first half and while defensive midfielders Nigel de Jong and Mark van Bommel snuffed out Slovak attacks and sprayed the ball wide, there was little attacking venom.
There was a glimpse of the team's potential in the 44th minute when Robben, Robin van Persie and Sneijder strung a succession of slick passes together to release van Bommel but van Persie screwed his fast, low cross wide of goal.
Robben again burst into life after the break, with almost a repeat of the first-half goal. He picked up a loose clearance on the right in the 50th minute, darted past two defenders again and unleashed a fierce left-foot shot that Mucha did well to turn round the post.
A minute later on the other side of the field, he crafted a superb chance for impressive defender Joris Mathijsen to double the lead from close range, but Mucha again saved well.
"We were preparing for three days for Robben, for his way of playing, but he is an absolute genius," said Slovakia coach Vladimir Weiss. "When I saw him in the line-up I knew he makes the Netherlands line-up 50 percent stronger and I was correct."
