Coach Jorge Luis Pinto praised Costa Rica's character after they overcame a second-half red card, conceding a late leveller and sustained pressure from Greece to reach their first ever World Cup quarter-final.
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Holland are next for Costa Rica after a topsy-turvy encounter in Recife, where they went ahead early in the second half through captain Bryan Ruiz's first-time strike.
That looked to be enough for Costa Rica, only for Greece defender Sokratis Papastathopoulos to net a stoppage-time leveller to take the round of 16 encounter into extra-time.
The match eventually went to penalties and, after man-of-the-match Keylor Navas saved Theofanis Gekas' attempt, Michael Umana struck home to send the Central Americans into the last eight.
"I am very happy," coach Pinto said after the 5-3 penalty shootout win.
"This is an incredible emotion that we all feel, this is an important win for the team and for the whole country. We are really proud.
"We are making history. It's beautiful what we have done. This win is for everyone in Costa Rica.
"We practiced penalties before and we had studied the opposition and that's why we scored 100 per cent.
"It was a dramatic match, a very difficult one. There were moments when we dominated the match but there were other moments when they did but we were strong and we came through."
As for Greece counterpart Fernando Santos, defeat was a tough pill to swallow in what is his last match at the Greece helm.
The Portuguese's contract with the Greek federation ends in the coming days and he will move on having led the Euro 2004 winners to the World Cup knockout stages for the first time ever.
"I don't really like talking about luck or lack of luck," Santos, sent to the stands before the shootout, said. "Costa Rica won, they were obviously happier.
"Obviously it can always go one side or another and it went to Costa Rica's, therefore they won and they go on. For that, they have to be congratulated.
"It is a sad moment for us because obviously we want to keep creating history and to make the Greek people even happier. That was not possible.
"When the fifth penalty went in I felt sadness, just sadness. Not much goes through your mind at that time. Immediately, you have a feeling of sadness.
"I wanted to continue, I wanted to go to Salvador, the team wanted to go to Salvador. It was a group feeling of sadness."