Robben leads Holland into quarterfinals
The Dutch went ahead in the 18th minute when Robben cut inside from the right flank and found the target with a low, precise shot from 20 meters (yards). Sneijder doubled the lead into an empty net in the 84th.
It was only a month ago when Robben and Sneijder were on opposite sides in the Champions League final, Robben with Bayern Munich and Sneijder with winner Inter Milan.
"We played a difficult match. Main thing is, we are through," Robben said. "Probably the perfect game has still to come."
Netherlands goalkeeper Maarten Stekelenburg preserved the win with two key saves in the 67th, and the Dutch extended their team-record unbeaten streak to 23 games.
"At a crucial stage Maarten Stekelenburg saved us," Netherlands coach Bert van Marwijk said.
In between the goals from Robben and Sneijder, the Dutch wasted numerous chances.
"We had a good first half hour. And we started well in the second half," Van Marwijk said. "We should have scored 2-0, 3-0, maybe 4-0 there."
In the quarterfinals, the Netherlands will face either five-time champion Brazil or Chile.
"We must play better against Brazil or Chile, that's for sure," Robben said.
Robert Vittek pulled one back for Slovakia from the penalty spot in injury time, tying him with Argentina forward Gonzalo Higuain for the tournament scoring lead with four goals.
Slovakia upset Italy 3-2 in its previous match, a result that eliminated the defending champions, and had to be satisfied with its tournament debut as an independent nation.
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"We played with heart and courage and we are proud that we made it to the second round, but the better team advanced," Slovakia coach Vladimir Weiss said. "The penalty made us feel a little better on the flight home."
Robben got his first start of the tournament, having injured his left hamstring on June 5 in the Netherlands' final warmup match against Hungary. He came on as a second-half substitute against Cameroon in the Netherlands' last group match and hit the post, after which Klaas Jan Huntelaar knocked in the rebound to seal a 2-1 win.
This time, Sneijder sent Robben sprinting upfield with a long, accurate pass and the winger did what he's been doing all season with Bayern - scoring with long shots from beyond the area.
"I was pretty free in my game," Robben said. "I know I'm not yet at my top level, but I was pretty confident today and that was a great pass by Wesley."
The Moses Mabhida Stadium was filled mostly with orange-clad Netherlands fans and they blasted their vuvuzelas on Robben's first touch. After the goal, the sound became deafening.
"It's fantastic," Van Marwijk said. "After such an injury that he has the touch to score a goal like that."
Weiss said he has been preparing his team specifically for Robben for three days.
"But he's a total genius, and when I saw him in the starting lineup I thought he makes the Dutch team 50 percent stronger - and I was right," the Slovakia coach said.
With a sharp breeze blowing in from the nearby Indian Ocean, Robben nearly doubled the lead in the 50th but goalkeeper Jan Mucha deflected his shot just wide of the goal. A minute later, Robben sent a dangerous cross inside the area and Mucha blocked a close-range effort from Joris Mathijsen.
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In the 71st, when he was replaced by Eljero Elia, Robben exited to a standing ovation.
Sneijder sealed the victory when Dirk Kuyt drew Mucha out of his net and had nobody to beat for his second goal of the tournament, also having found the target in a 1-0 win over Japan.
Slovakia was awarded a penalty in the third minute of injury time, when substitute Martin Jakubko was taken down inside the area.
Otherwise, Slovakia's two best chances both came in the 67th. Stekelenburg leaped to tip a powerful shot from Miroslav Stoch over the crossbar and then Vittek, who scored twice against Italy, directed his shot too close to the Netherlands goalkeeper seconds later.
The Netherlands also won all three of its group games, with its last loss coming to Australia in September 2008, a run of 18 wins and five draws.
The Netherlands reached consecutive World Cup finals in 1974 and 1978 but lost both - to Germany and Argentina, respectively. Its only major tournament victory was the 1988 European Championship.
Netherlands: Maarten Stekelenburg, Gregory van der Wiel, John Heitinga, Joris Mathijsen, Giovanni van Bronckhorst, Dirk Kuyt, Mark van Bommel, Wesley Sneijder (Ibrahim Afellay, 90), Nigel de Jong, Arjen Robben (Eljero Elia, 71), Robin van Persie (Klaas Jan Huntelaar, 80).
Slovakia: Jan Mucha, Peter Pekarik, Martin Skrtel, Radoslav Zabavnik (Martin Jakubko, 88), Jan Durica, Miroslav Stoch, Juraj Kucka, Vladimir Weiss, Marek Hamsik, Robert Vittek, Erik Jendrisek (Kamil Kopunek, 71).