كتب : Omar AbdelAziz
Wesley Sneijder inspired the Oranje with a late goal and an assist to Arjen Robben's opener.
Robert Vittek converted a late penalty to become the tournament's joint top scorer, leveling on four goals with Gonzalo Higuain.
The Dutch will play the winner of the match between Brazil and Chile.
Robben opener
For the first time in South Africa, star man Robben was fit to feature in the Oranje starting eleven at the expense of Rafael van der Vaart.
The flying winger was off the mark after 18 minutes, scoring a trade-mark strike from 20 yards out after cutting inside from the right flank, following a terrific through ball by Sneijder.
The first half was uneventful as Slovakia did little to respond to their trailing, with Holland hardly making an attempt to kill of the game.
Sneijder killer
Robben almost scored a typical second four minutes after the break, but Jan Mucha made a superb full-stretch stave to deny him, before thwarting Jan Mathijsen with another great stop.
The Dutch then sit back waiting for a Slovakia opening that finally came after the hour mark with two quick shots from Miroslav Stoch and Vittek, both denied brilliantly by Marten Stekelenburg.
The Slovaks were punished in the 83rd minute when Holland snatched a killer goal to end book their quarter-finals ticket.
A quick freekick sent Dirk Kuyt through on goal before Mucha interfered, but the Holland forward regained the ball to set up Sneijder, who slotted home in an empty net.
With 30 second to go, Slovakia earned a late penalty when Stekelenburg brought down Slovakia substitute Martin Jakubko as Vittek made no mistake from the last kick of the game.