The Newcastle goalkeeper saved spot kicks from Costa Rica captain Bryan Ruiz and Michael Umana after the match had finished 0-0.
The Dutch will face Argentina in the semifinals 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.
Argentina 1, Belgium 0: Gonzalo Higuain’s first goal of this World Cup sent Argentina into the semifinals with a win over disappointing Belgium.
Argentina, which hadn’t advanced past the World Cup quarterfinals since 1990, put in its best performance so far in the tournament, controlling the match after Higuain’s eighth-minute goal.
The Napoli striker fired home Angel Di Maria’s deflected pass just inside the area, beating Belgium goalkeeper Thibaut Courtois with a low shot to the far corner of the net.
Higuain came close to making it 2-0 in the second half when his shot smashed into the crossbar. Lionel Messi missed a chance to score his fifth goal of the tournament in stoppage time when Courtois stopped his shot.
Belgium lacked the creativity to find a way past Argentina’s defensive line, and created few clear chances apart from a pair of headers by Kevin Mirallas and Marouane Fellaini.
Argentina was knocked out in the quarterfinals in the previous two World Cups, both times by Germany. The last time it reached the semifinal stage was 24 years ago in Italy, when Diego Maradona led the team to the final, which it lost 1-0 to West Germany.
In Brasilia on Saturday, Argentina never lost control even after Di Maria — the team’s most influential player in Brazil aside from Messi — was substituted by Enzo Perez in the 33rd. The winger had appeared to hurt his right leg while taking a shot five minutes earlier.
Argentina took the lead when Di Maria picking up a pass from Messi, cut in from the right and tried to find fullback Pablo Zabaleta, but his pass bounced off Jan Vertonghen into Higuain’s path.
The Napoli striker avenged himself for a string of mediocre performances in Brazil and was Argentina’s best player before being substituted by Fernando Gago in the 81st.