Winston Parks scored a stunning goal early in the second half to condemn Switzerland to their third successive friendly defeat - all at home - since they clinched their place in South Africa.
Switzerland, jeered off the field at the Tourbillon stadium, also lost 1-0 to Norway in November and 3-1 to Uruguay in March.
Their form against Latin teams is especially worrying as they face Honduras, Chile and Spain in their World Cup group.
Costa Rica goalkeeper Keylor Navas was a bored spectator for most of the game as the Swiss barely mustered a clearcut chance, apart from a desperate flurry in the closing stages.
The Central Americans played the more fluid football in a generally scrappy game and gave they impression that they should be heading for South Africa rather than the lacklustre Swiss.
"The scored their goal with one striker against three defenders," said Switzerland coach Ottmar Hitzfeld, clearly angry with his defence. "But the team reacted well after that and created some chances.
"You're always disappointed when you don't win but it was a good test," added the former Bayern Munich and Borussia Dortmund coach, whose team host Italy on Saturday in their final warm-up.
The visitors took control early in the second half when Carlos Hernandez was close with a long-range shot and Cristian Bolanos tested Diego Benaglio with a powerful drive after cutting inside his marker.
The goal came in the 55th minute when Romanian-based Parks picked up the ball just inside his own half and, despite being faced by three defenders, managed to force his way through to score with an unstoppable shot from the edge of the area.
Switzerland had to wait for stoppage time for their best chance when otherwise ineffective captain Alexander Frei had a shot parried by Navas and Eren Derdiyok shot wide from the rebound with the goalkeeper out of his ground.
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