Neither side could break the deadlock in 120 minutes of football, but the Dutch booked their spot in the last four after coming through 4-3 on penalties against their spirited opponents.
Louis van Gaal's side will face Argentina in the second semi-final on Wednesday.
Here, Sports Mole dissects what was an incredible night of football in Salvador.
On target: 15
On target: 3
Was the result fair?
Where to start? For long spells, it was not the most entertaining match. Both sides struggled to create clear openings in the final third, but it is difficult to argue that Netherlands did not deserve to come through. Statistics rarely paint a false picture and Netherlands were superior in almost every area this evening. They indeed had the better chances and but for some brilliant goalkeeping from Keylor Navas, the match would more than likely have ended in normal time. Costa Rica will look to some refereeing decisions in extra-time, however, especially a challenge from Ron Vlaar on Marco Urena, which might have brought a penalty. It was always going to be difficult for the loser to take after such an incredible effort from both teams, but on the balance of play, Netherlands deserved to advance into the final four of the tournament.
The Dutch have played some brilliant football this summer, but that was not really the case this evening. Dirk Kuyt and Memphis Depay were deployed in wide areas by Van Gaal, but neither influenced proceedings in the final third. Robin van Persie also struggled to produce his best form and was guilty of missing a couple of golden chances late on. That said, aside from a couple of uncomfortable moments, Netherlands were solid in defensive areas and had control of the possession for long spells of the 120 minutes. On another night, they would have come through comfortable winners, but inspired goalkeeping from Navas and some poor finishing forced extra-time. Van Gaal made an incredible call by bringing on Newcastle United stopper Tim Krul for the spot-kicks and the goalkeeper saved two in the shootout to help his side into the next round. It was far from impressive from the 2010 finalists, but they are in to another World Cup semi-final.
Costa Rica's performance
It is difficult to think of any more superlatives for this Costa Rica team. They were expected to finish bottom of a group that included Uruguay, Italy and England, but instead topped the section before beating Greece in the last round. It had been feared that they would struggle against the Dutch, but that was simply not the case. They had to surrender possession for long spells, but remained a threat on the counter-attack and were once more incredibly sound in defensive areas. On paper, the two teams just did not compare, but Costa Rica had not read the script once more and produced another fighting performance. They had to ride their luck for long spells and rely on some heroics from Navas, but they forced the lottery of penalties. It just wasn't to be at the end of the evening, but it has taken nothing away from their excursions this summer. In particular, Navas, Giancarlo Gonzalez and Yeltsin Tejeda were wonderful for their side this evening.
Sports Mole's man of the match
Giancarlo Gonzalez: Navas will rightly get the headlines for Costa Rica's incredible performance this summer, but Gonzalez has been right up there with the Levante goalkeeper. Again this evening, Gonzalez was just terrific. Not only was the 26-year-old aerially dominant and strong in the tackle, he also showed his willingess to play out from the back. It was just about as good a defensive performance as has been seen at this World Cup. His club team Colombus Crew could have a busy few weeks with calls from interested clubs.
Netherlands came through in the end, but they missed a number of golden chances in the latter stages of normal time as Costa Rica began to tire. The best of those fell to Van Persie following a wonderful pass from Wesley Sneijder, but somehow the Manchester United striker failed to find the back of the net - producing a fresh-air shot in the process. It should have ended the contest, but the Dutch were made to wait for spot-kicks to book their spot in the final four.
Overall, it was a difficult night for referee Ravshan Irmatov. The 36-year-old perhaps should have awarded Costa Rica a penalty in extra time when Vlaar seemingly felled Urena inside the box, but Iramatov was not interested. The official was also guilty of being too lenient during certain periods of the match, with Costa Rica's Junior Diaz perhaps lucky to escape a red card after committing a couple of late challenges having already been booked. Overall, six bookings were awarded by Iramatov.
Netherlands: The Dutch face Argentina in the second semi-final on Wednesday. Should they advance, their opponents in the final would be either Brazil or Germany, who meet on Tuesday.
Costa Rica: As it stands, Costa Rica have no confirmed fixtures on their agenda. However, one thing is for certain, all their players and coaching staff have earned a rest.