The Central Americans avoided being the only team to go home from Russian Federation without a goal when defender Kendall Waston rose to head in a corner early in the second half to equalise at 1-1.
Josip Drmic put the Swiss 2-1 up, but an injury-time penalty by Bryan Ruiz hit the bar and bounced in off Swiss keeper Yann Sommer to secure a point for the Central Americans. "We are quite ambitious, we want more and more as we move along and it is very important to show that also and I have no doubt at all that we can perform better against Sweden", he added. Read the text online broadcast of the match Switzerland - Costa Rica.
Captain Stephan Lichtsteiner and Fabian Schaer - who have nearly 150 caps between them - are ruled out of the match on July 3 after both picked up a second yellow card for the tournament on Wednesday.
The Swiss looked in cruise control but Costa Rica carved out two decent chances early on the second half. The goal went down as an own goal, despite the fact that it saved Costa Rica's blushes by earning the Ticos their first point of the 2018 World Cup.
Navas was called into action shortly after, blocking Embolo's acute effort at his near post, before Waston deservedly pulled Costa Rica level after 56 minutes.
The Swiss drew 1-1 against Brazil in their first group game but overturned a one-goal deficit to defeat Serbia 2-1 in their second group game and needed a draw or win to reach the round of 16.
Costa Rica, on the other hand, will be looking to wrap up their 2018 FIFA World Cup journey with a victory after failing to enter the Round of 16.
Josip Drmic thought he'd scored the victor for Switzerland in the 88th minute, but the Central American side were able to earn a point after a penalty in stoppage time. Ruiz stepped up to score his 25th global goal, but he struck the woodwork and it bounced into the net off Sommer.
Costa Rica may be going home tomorrow, but you'd never know that from their fans in the stadium.
Ruiz did get a chance from the spot in the third minute of stoppage time when Campbell was felled in the box, his penalty thumping back off the crossbar and against Sommer's head to complete a frantic finale.