After losing 1-0 to England on Saturday, the Spanish looked toothless in attack and vulnerable in defence in the first half of a rain-lashed match in San Jose, falling two goals behind at the break before raising their game in the second.
Captain Iker Casillas committed an uncharacteristic howler to gift the home side the lead on the day the 30-year-old set a new appearances record for the national team of 127.
The Real Madrid goalkeeper miscontrolled the ball near the edge of the penalty area just after the half-hour, surrendering possession to Randall Brenes and allowing the Costa Rica forward space to lift the ball into the empty net.
The home side doubled their lead just before half-time in the Costa Rican capital when Joel Campbell was given too much space on the right and curled a fine left-foot effort past Casillas from distance.
Cesc Fabregas had two decent chances for Spain in the first half, both from Andres Iniesta passes, but Vicente del Bosque's team looked a shadow of the side that claimed a first World Cup in South Africa last year.
Since their triumph in Johannesburg, Spain have lost friendlies against Argentina, Portugal, Italy and England, although they won all eight of their Euro 2012 qualifiers.
The Iberians showed more urgency in the second half and Iniesta sent an effort narrowly over the crossbar after a weaving run into the area before David Villa drew a fine save from Keilor Navas with a powerfully-struck free-kick.
Del Bosque threw on Fernando Torres, David Silva, Santi Cazorla and Jesus Navas and as Spain mounted attack after attack Silva finally found the net in the 83rd minute before Villa nodded in a Santi Cazorla free-kick for the equaliser.
