Substitute goalkeeper goalkeeper Tim Krul, introduced just for the shootout, saved from Bryan Ruiz and Michael Umana as the Netherlands triumphed 4-3.
Costa Rica defended deeply from the start and goalkeeper Keylor Navas, whose performances have played a large part in his country's run to the quarter-finals for the first time, was again in sharp form with a series of saves, while Wesley Sneijder hit a post with an 81st-minute free kick and Robin van Persie had a scrambled shot cleared off the line in stoppage time of normal time.
The game blew wide open in extra time as Marcos Urena had a chance to win it for Costa Rica but had a shot well saved by Jasper Cillessen, while Sneijder hit the bar two minutes from the end.