The Dutch never could find a way past Keylor Navas, but advanced to the semifinals after taking a 4-3 win on penalties.
Tim Krul was an unlikely hero as the Netherlands secured a 4-3 shootout win over Costa Rica to book a FIFA World Cup semifinal place.
Over 120 goalless minutes in Salvador, Louis van Gaal's team struck the post or crossbar on three occasions and the Manchester United-bound manager unleashed an unexpected secret weapon from the bench during the dying seconds of extra time.
Krul, who has an unremarkable penalty record at Newcastle United, came on for Jasper Cillessen to save Costa Rica's second and last penalties from Celso Borges and Michael Umana. Robin van Persie, Arjen Robben, Wesley Sneijder and Dirk Kuyt were the Netherlands' flawless foursome.
It ends a remarkable journey for Costa Rica, which won a group featuring Uruguay, Italy and England before beating Greece on spot kicks. But this proved a step too far as the Dutch, who had lost four of their previous five shootouts in major tournaments, banished their demons from 12 yards to book a semifinal appointment with Argentina
Costa Rica combined the organization and attacking verve that has been the team's hallmark in Brazil, but ambition going forward left the Ticos exposed to the Netherlands' incision on the break and indebted to inspirational goalkeeper Keylor Navas.
Jorge Luis Pinto's team was in a confident mood as the game entered its final stages before Sneijder rattled the post from a free kick to herald a late onslaught.
But Van Persie proved uncharacteristically wasteful in spurning three goalscoring opportunities, including one close-range sitter, as the Netherlands failed in a bid to avoid an extra half hour.
Sneijder crashed a shot into the bar, while Costa Rica substitute Michael Urena threatened to snatch the headlines that would ultimately be Krul's.
Memphis Depay, starting having twice netted from the bench in this tournament, gave Van Persie the game's first clear opening in the 21st minute but Navas closed the angle well and stopped Sneijder's follow up.
Navas saved well in the 29th minute as Van Persie and Depay reversed their earlier roles, while a frantic Dutch clearance as Johnny Acosta looked to turn home Celso Borges' set piece knockdown underlined a developing end-to-end feel.
Sneijder took a more direct approach from a 38th-minute free kick, conceded by Junior Diaz, but Navas - quelled fears surrounding a shoulder injury that dogged him earlier in the week - clawed superbly around the post.
Robben's admission that he dived during the Netherlands' win over Mexico in the previous round dominated the pre-match build-up and Umana followed Diaz into the book after he too fouled the forward, who cleverly set up Sneijder to blaze over from the resulting 53rd-minute set play.PHOTOS: U.S. fan reactions | Beautiful people in Brazil
It was Joel Campbell and not his illustrious opponent who went to ground easily in the 60th minute as a promising Diaz raid down the left came to nothing, before Giancarlo Gonzalez headed over from another fine Christian Bolanos delivery to increase Dutch anxiety.
There was contact from Gonzalez and another booking as Robben went to ground theatrically in the 81st minute. Sneijder watched his free kick from the left-hand corner of the area cannon back off the post.
Van Persie was then denied by Navas and he somehow failed to connect with Sneijder's delicious 88th-minute cross.
The Manchester United man was not done there and - after Navas punched his free kick away in stoppage time - Costa Rica midfielder Yeltsin Tejeda cleared Van Persie's shot off the goal line via the crossbar, Daley Blind's low center having caused complete chaos.
The start of extra time brought little let-up and Navas produced further acrobatics to keep out Ron Vlaar's header, but a flap at the resulting corner showed the Levante man was not infallible.
Vlaar was unimpressed as Urena sought a penalty at his expense, although Pinto's men were restricted to a largely defensive brief as the additional period progressed.
Urena crafted his team's best chance, drawing a nerveless 117th-minute save from Cillessen at the end of a jinking run and penalties arrived after Sneijder rattled the crossbar from distance with Navas rooted to the spot.
When the heat was on from 12 yards shortly afterwards, Krul was anything but.