A first-half goal from Diego Lugano gave Oscar Tabarez's side strong hopes of playing in South Africa next year, following their failure to qualify for the 2006 finals in Germany.
The Ticos could not make their home advantage pay, failing to get into the Uruguay box or test Fernando Muslera. Costa Rica suffered a further blow in the 20th minute when defender Gilberto Martinez was forced off with an injury after colliding with Alvaro Fernandez.
While he was off receiving treatment, Uruguay profited. Lugano headed goalwards from a corner, and although his first effort was blocked, the ball came back to him and he beat Navas from an awkward position.
Costa Rica did have a chance to equalise just before half-time, but Bryan Ruiz's header went over the crossbar from Randall Azofeifa's cross. Things got even worse for Rene Simoes' side seven minutes into the second half as Azofeifa brought down Fernandez and earned a second yellow card and an early shower.
However, where they had punished Costa Rica's momentary short-handedness in the first half, Uruguay showed little ability to take advantage a second time. They squandered possession too often and failed to create chances.
Costa Rica were showing more purpose, but their shots, coming from Alvaro Saborio and Walter Centeno, were too weak to properly test Muslera. Fernandez could have doubled Uruguay's lead with three minutes to go, but saw his header blocked by Junior Diaz.
That means Uruguay take a slim but significant advantage into the rematch at the Estadio Centenario in Montevideo on Wednesday night.