Costa Rica drew 1-1 in Kingston against Jamaica, taking them to 15 points, and with Honduras drawing 2-2 at home to Panama, none of the other four teams in the group can push the leading duo out of the top three automatic qualifying spots.
Mexico, next to bottom in the six-team standings, have eight points, as do a Panama team that has never qualified for the sport's biggest tournament.
Honduras currently occupy third place on 11 points but with two rounds of games to come in October, the battle for the final automatic spot and fourth-place, which offers a play-off against Oceania winners New Zealand, is set to go down to the wire.
Both the Americans and Costa Rica had to wait an hour after their games finished to be certain that their positions were unassailable, as both needed Honduras to get at least a point at home to Panama.
Costa Rica's mood was soured by the concession of an injury time equaliser - Jermaine Anderson scoring for Jamaica to cancel out Randall Brenes's 75th minute opener.
Then there was some tension after Panama equalised through Gabriel Torres' second goal in the final seconds of the game but the point for Honduras set off the party.
Costa Rica coach Jorge Luis Pinto broke down sobbing during an interview with local radio station Columbia.
"I've worked all my life, so hard, to make it to the World Cup, all my life... this is sheer happiness," he said before the tears overwhelmed him.
Klinsmann, a World Cup winner with West Germany as a player in 1990, was a little more restrained in his reaction but still delighted to be making a second trip to the finals as a coach following his run to the last four with Germany in 2006.
"It's a huge milestone whenever you make it to the World Cup, the biggest competition in this sport, especially hosted in Brazil, one of the biggest soccer nations," he said. "It means a lot to all of us. To our fans and to this country as well".
Mexico face a must-win match with Panama on October 10 and they will need to somehow pick themselves up from an abject second half display in Columbus.
"I don't know what to tell you, we're in debt with the people and very ashamed," midfielder Christian Gimenez told Mexico's TV Azteca.
- Sports & Recreation
- Costa Rica
- Juergen Klinsmann