The Ticos made a blistering start and had established a 2-0 lead inside 10 minutes thanks to headers from Jhonny Acosta and Celso Borges.
The USA threatened a comeback when Costa Roca goalkeeper Keylor Navas fouled Fabian Johnson in the box and Clint Dempsey, on his 100th appearance for the visitors, scored from the spot to halve the arrears two minutes before half-time.
New Seattle signing Dempsey hit the post on the hour mark as the USA threatened an equaliser but they could not find it and Joel Campbell put the game beyond them with 15 minutes to go.
The win moved Costa Rica to the summit, a point ahead of the US.
Honduras climbed to third, three points further back, after a stunning 2-1 win in Mexico.
There was no sign of a shock when Giovani Dos Santos provided Oribe Peralta with the chance to put Mexico one up after five minutes.
But the hosts became sloppy, Jerry Bengston capitalising on some slack defending to equalise after 64 minutes and two minutes later Carlos Costly swooped on Diego Reyes' mistake to give Honduras a lead they would not relinquish.
Panama's hopes of qualification suffered a blow when they could only manage a goalless draw at home to Jamaica.
On Tuesday, Jamaica meet Costa Rica, the USA host Mexico and Honduras take on Panama.
The top three teams qualify for Brazil 2014 with the side finishing fourth having to settle for an intercontinental play-off against New Zealand.