Costa Rica took the lead two minutes before half time when Johan Venegas rose unchallenged to glance home a Christian Bolanos cross.
The home side gunned for goals after the break and did not have to try too hard against a team that looked all at sea in an atrocious second half.
Bolanos scored after 69 minutes when he got on the end of a lovely curling cross from Bryan Ruiz and five minutes later substitute Joel Campbell wrapped up the three points with a nice solo goal.
The Arsenal striker on loan to Sporting Lisbon rubbed salt into the U.S. wound when he added a fourth three minutes later.
The result leaves Klinsmann's U.S. bottom of the six-team group alongside Trinidad and Tobago.
Costa Rica, meanwhile, top the so-called Hexagonal, the only side to win both their opening games.
The top three teams after the 10 home-and-away matches qualify automatically for Russia 2018, while the fourth-placed side goes into a play-off with a team from Asia.
Mexico, who drew 0-0 with Panama in a dull match in the isthmus, have four points, the same as Panama.
In the evening's earlier game, Honduras got their first points with a comprehensive 3-1 win over Trinidad and Tobago.
Romell Quioto and Emilio Izaguirre put Honduras in the driving seat with early goals and although Carlyle Mitchell pulled one back for the visitors after half-time, Eddie Hernandez scored a third for Honduras with 10 minutes remaining.
(Writing by Andrew Downie)
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