RECIFE, Brazil — With his team down to 10 men for nearly an hour, Keylor Navas made sure Costa Rica’s last line of defense held firm.
The goalkeeper came through with a string of stops in regulation and extra time and then made the only save in a penalty shootout to send Costa Rica through to the World Cup quarterfinals for the first time on Sunday with a win over Greece.
After Navas dived to his right to push out the effort by Theofanis Gekas, Costa Rica defender Michael Umana scored the decisive spot kick for a 5-3 win in the shootout, sending the team sprinting down the field to embrace its goalkeeper. The game had finished 1-1 following extra time, after Greece equalized in second-half injury time.
‘‘It was only a dream for us, a dream that became a reality,’’ Navas said. ‘‘A dream that was dreamt by an entire country.’’
Costa Rica will play one of the tournament favorites, the Netherlands, in the quarterfinals on Saturday in a surprising appearance in the last eight for the small country that has a quarter of the population of Brazil’s biggest city and which hardly anyone picked to even make it past the group stage.
‘‘To the entire people in Costa Rica, those at home and out on the streets, this is for you,’’ Costa Rica’s Colombian coach Jorge Luis Pinto said. ‘‘This is a people that love football and they deserve it . . . We will continue fighting. We will go on. We see beautiful things.’’
The victory also delighted the majority of the 41,000-plus fans on hand as the Brazilian locals shouted for Costa Rica throughout the game and often broke out into chants of ‘‘Ole, Ole, Ole, Ole, Ticos!’’ — using the common nickname for Costa Ricans.
Greece was often booed.
Costa Rica went ahead in the 52d minute with a coolly taken goal by captain Bryan Ruiz, but the game changed when Oscar Duarte clumsily lunged at Greece’s Jose Halebos in the 66th and was sent off with a second yellow card.
Pouring forward, the Greeks did beat Navas in injury time when defender Sokratis Papastathopoulos smashed in a rebound to make the team’s numerical advantage eventually pay. Yet Navas kept denying the Greeks through extra time and then, crucially, when he dived, threw up a hand, and pushed Gekas’s spot kick away at the end.
‘‘Obviously he has to be congratulated,’’ Greece coach Fernando Santos said of Costa Rica’s goalkeeper. ‘‘If it weren’t for [him], the results would have been different.’’
The red card for Duarte changed the game — which Costa Rica had slowly begun to control — and Greece surged forward for most of the remainder of the match.
But, with the exception of Papastathopoulos’s goal, they just couldn’t get past Navas as shot after shot was blocked. Greece had 13 shots on target to Costa Rica’s two.
Navas smothered a volley from Dimitris Salpingidis from point-blank range in the first half. After the equalizer, he threw himself high to tip over a header from substitute Konstantinos Mitroglou that would have surely been the winner in the dying seconds of regulation time. He then made three crucial stops in extra time, when Costas Katsouranis, Lazaros Christodoulopoulos, and Mitroglou were all denied.
During the shootout, the Costa Rican squad had knelt in a line. They then burst onto their feet to race over to Navas and smother him in a huddle when Umana’s shot hit the net.
‘‘We will not stay on the quarterfinals,’’ Pinto said. ‘‘Rest assured that we will not get eliminated there.’’