The Newcastle goalkeeper saved spot kicks from Costa Rica captain Bryan Ruiz and Michael Umana after the match had finished 0-0.
The Dutch team will next face Argentina in the semifinals on Wednesday in Sao Paulo.
In another stroke of tactical genius at this year’s World Cup, Netherlands coach Louis van Gaal pulled Jasper Cillessen moments after the Ajax goalkeeper had kept his team in the match by saving a shot from Marcos Urena in extra time.
Krul looked super confident during the shootout, saving the second and fifth penalties.
When Krul stopped Ruiz’s penalty, Cillessen, watching from the sideline, punched the air in celebration.
Costa Rica goalkeeper Keylor Navas had kept his team in the match with a string of saves in the first half and again in extra time. When Wesley Sneijder twice beat him late in regulation and again in the second half of extra time, the woodwork made the stop.
Sneijder hit the post with a free kick in the 80th minute and sent a curling shot over Navas and off the crossbar before the penalty shootout.
At the end, however, Navas could not stop any of the four Dutch penalties as Robin van Persie, Arjen Robben, Sneijder and Dirk Kuyt all scored.