The Bayern Munich winger, recalled to the starting line-up after overcoming a hamstring problem, blazed a low shot into the bottom corner in the 18th minute before Wesley Sneijder doubled the advantage eight minutes from time as the Netherlands secured their fourth straight victory in the finals.
Slovakia pulled a goal back from the penalty spot through Robert Vittek with the last kick of the game to at least finish their campaign on a positive note.
Holland manager Bert van Marwijk will be hoping the impressive run proves to be a lucky omen considering the last time the Netherlands secured four successive wins they went on to reach the final in 1974.
Slovakia started well and spurned a brace of early chances before spending the remainder of the game toiling to keep their opponents in check.
Erik Jendrisek shot just over the crossbar in the opening two minutes and Marek Hamsik also fired just wide. But the Netherlands were content to soak up the pressure and break from deep, with the pace of Robin van Persie and Robben a constant threat.
Sneijder and Van Persie both wasted golden opportunities to break the deadlock as the Netherlands began to exert their superiority on the contest and it came as no surprise when Robben opened the scoring with a fine individual effort.
He is supposed to have a suspect hamstring but there seemed no problem as he sped down the wing before cutting inside in trademark fashion and drilling a low drive into the bottom corner.
Robben's brilliance left Slovakia with a mountain to climb. They stuck to the task well and showed admirable spirit and commitment, but Van Marwijk's side were always in control and seemed content to protect their lead, even if their lack of desire to kill the game off will be of slight concern to supporters.
They had to rely on a mistake from Jan Mucha to allow Sneijder to make it 2-0 on 82 minutes and even though Vittek pulled one back in stoppage time there was no way back for the Slovakians.
Manager Vladimir Weiss will be disappointed but he shouldn't be. Slovakia over-achieved to get beyond the group stage and the memories of beating current holders Italy can be cherished forever.
Netherlands (4-5-1): Stekelenburg; Van Der Weil, Heitinga, Mathijsen, Van Bronckhorst; Kuyt, Van Bommel, Sneijder (Afellay 90), De Jong, Robben (Elia 71); Van Persie (Huntelaar 80).
Slovakia (4-4-2): Mucha; Pekarik, Skrtel, Durica, Zabavnik (Jakubko 86); Stoch, Weiss, Kucka, Jendrisek (Kopunek 72); Vittek, Hamsik (Sapara 86).