Jurgen Klinsmann's men lost for the first time since May, finding the Ticos' new Estadio Nacional no kinder to visit than Saprissa, where they lost a qualifier in 2009
Johnny Acosta, Celso Borges and Joel Campbell struck for the Ticos, while Clint Dempsey converted a penalty kick for the visitors, who tasted defeat for the first time since May.
The Americans were dealt a tough blow before the match even began, with midfield stalwart Michael Bradley limping off the field following warm-ups and being replaced in the lineup by Geoff Cameron.
Matters didn't get any better once the game started. Costa Rica didn't wait to put the United States under pressure, with Bryan Ruiz getting behind the American defence in the second minute but having his close-range effort pushed aside by Tim Howard.
It ultimately mattered not, as the Ticos scored on the subsequent corner kick. Making a near post run, Acosta nodded a shot that glanced off the head of DaMarcus Beasley, who was manning the post, and flew into the net.
Just seven minutes later Costa Rica doubled their advantage. Overpowering Beasley, Borges charged onto a cross from Christian Bolanos and headed a shot home.
The Americans pulled one back three minutes before half-time. Running onto a chip from Graham Zusi, Fabian Johnson and goalkeeper Keylor Navas collided at the top of the box, leading the referee to point to spot. Going for power over placement, Dempsey, on his 100th cap, hit his penalty off Navas and in.
In the 57th minute, Dempsey nearly got the equaliser when his effort from just outside the box crashed off the post.
But Costa Rica made the game safe in the 75th minute when Campbell ran onto a clearance, outran Matt Besler and slotted in a shot that slipped through Howard's legs.
The USA resume qualifying on Tuesday with a crucial match against bitter rivals Mexico in Columbus, without the suspended trio of Matt Besler, Cameron and Jozy Altidore.