The Concacaf side have been the surprise package of the tournament so far and will fancy their chances of making it to the quarter-finals
And the chances of it taking place in the 2014 competition in Brazil were even more unlikely after Fifa drew the groups in December last year.
But Costa Rica, widely expected to be the weakest team of Group C, have shocked the football world with wins over Uruguay and Italy.
And those results – along with a 0-0 draw against England – saw them not only reach the last 16, but do it in style - topping their pool.
The 28th-ranked nation entered the World Cup with just two wins from their previous nine matches, hardly form to inspire Jorge Luis Pinto's side.
But the likes of attackers Joel Campbell and Bryan Ruiz, as well as defensive pair Oscar Duarte and Junior Diaz, have thrived on the big stage in Brazil.
With their qualification guaranteed after their first two wins, Pinto has had more than a week to contemplate the pressure of knockout football ahead of Sunday's clash in Recife.
And although Ticos midfielder Yeltsin Tejeda has expressed surprise at facing Greece, who secured their berth in the round of 16 with a last-gasp 2-1 win over Ivory Coast, he insisted his side will be prepared.
"We were thinking more about [playing] Colombia and the Ivory Coast," Tejeda said.
"And in the end came the least expected team. Now we have to change the videotape."
Costa Rica have never gone beyond the last 16 at a World Cup, while Greece made history by progressing through the group stage for the first time.
Greece's last 16 hopes looked in tatters after a 3-0 defeat to Colombia in their first match in Brazil.
A goalless draw against Japan did little to improve their chances, but Greece then surprised the Ivory Coast in Fortaleza.
Greece – who were denied by the woodwork on three occasions – took the lead before being pegged back by Wilfried Bony 16 minutes from time.
Only a victory would have seen Greece through and Giovanni Sio's trip on Georgios Samaras gave them a chance in injury time.
Samaras, who had not scored in over two years for his national side, showed nerves of steel to calmly slot the 93rd-minute penalty and coach Fernando Santos believes the victory made a mockery of the claims that Greece cannot attack.
"We showed against Ivory Coast how well we can defend but also how good we can be in attack," he said.
"We created a lot of chances and we kept attacking until the end. Even when we conceded the 74th-minute equaliser, we continued to attack."
Goalkeeper Orestis Karnezis and defender Panagiotis Kone were both substituted with injuries in the first half against the Ivory Coast.
Karnezis is likely to be fit for this clash, but Kone's involvement is doubtful.
Greece captain Kostas Katsouranis is also available for selection after serving a suspension.