Jorge Luis Pinto's side battled to another astounding victory as they secured a shoot-out triumph despite playing close to an hour with 10 men
Earmarked as whipping boys having been drawn alongside England, Italy and Uruguay in Group D, Jorge Luis Pinto's men shocked the world by winning the pool with a haul of seven points.
And another chapter was written in their remarkable story in Recife on Sunday as, following a 1-1 draw over 120 minutes, they triumphed in the shootout against a Greece side who know all about beating the odds following their Euro 2004 victory 10 years ago.
That Costa Rica even forced spot-kicks was incredible given they suffered the heartbreak of seeing Sokratis Papastathopoulos force extra time with a last-gasp strike.
At that stage, it appeared Oscar Duarte's 66th-minute sending off, which came after Bryan Ruiz put the South Americans ahead, would prove decisive.
But having produced a string of stunning saves to deny Greece in outfield play, Keylor Navas was the hero of the shootout as he kept out Theofanis Gekas' effort.
Despite the pressure of attempting to take Costa Rica to the quarter-finals for the first time, Michael Umana then coolly converted to set up a last-eight meeting with Netherlands.
The game initially lived up to its billing of vibrant attack meeting dogged defence as Costa Rica surged forward with verve.
Costa Rica's endeavour almost brought early reward, too, when Christian Bolanos powerfully struck over from a tight angle.
Greece enjoyed a good spell themselves thereafter, although their final ball left a lot to be desired.
That was also the story at the other end as Costa Rica failed to make the most of good openings with the match becoming increasingly stretched.
That was the sole bright moment of a largely turgid first period, yet Costa Rica ensured the second would be decidedly more exciting by scoring in the 52nd minute.
Ruiz was the man to find the net, his fortuitous finish from 20 yards wrong-footing goalkeeper Orestis Karnezis following Bolanos' slide-rule pass.
Seemingly holding all of the aces at that stage, Costa Rica were reduced to 10 men midway through the second period when Duarte was sent off for a second bookable offence following an ill-judged sliding challenge on Holebas.
Suddenly sparked into life, Greece pressed forward in numbers and got their equaliser in the 91st minute when Papastathopoulos rifled home after Navas had produced a fine save to deny Gekas.
Costa Rican disappointment quickly turned to relief, however, when Navas produced a stunning save to turn Konstantinos Mitroglou's header over the crossbar.
Inspired by the efforts of their goalkeeper, Costa Rica's defenders were similarly heroic in the first period of extra-time, producing a host of crucial late blocks.
Remarkably, it was the 10 men prospering in the second half - although Greece missed the best chance when Lazaros Christodoulopoulos hit straight at Navas following a quick counterattack in which Fernando Santos' side had a five-on-two chance in their favour.
There was still time for one last opening, too, as Navas produced another fine save, this time denying Mitroglou from point-blank range.
An impressive shootout ensued as the first seven were converted until Navas athletically kept out Gekas.
Umana then made no mistake, his conversion sending the Costa Rican supporters into delirium.