Brian McBride and Landon Donovan both scored in a 2-0 win over Mexico to put the United States through to the quarter-finals of the 2002 World Cup.
The U.S. won an elimination game for the first time in the World Cup and will meet Germany at Ulsan on Friday.
McBride hit the back of the net in the eighth minute following a run by captain Claudio Reyna on the right side. McBride picked the far corner through Mexican defenders for his 20th international goal.
Donovan finished a counterattack by Eddie Lewis on the left in the 65th minute with a header for his second goal of the tournament.
"Our guys left everything on the field. I'm real proud of them," American coach Bruce Arena said. "It's a great day for U.S. soccer."
The U.S. last had a cleansheet in the World Cup against England (1-0) in a group match in 1950, considered one of the biggest upsets in World Cup history. In adddition, the U.S. did play in the semi-finals of the 1930 inaugural World Cup in Uruguay, but that was under a different format and with just 13 teams participating.
Despite owning the advantage in ball possession and pressure much of the game, Mexico were unable to get anything by veteran keeper Brad Friedel.
Ramon Morales made the first attempt after 15 minutes with a drive just wide of the left post.
Cuauhtemoc Blanco had the best opportunity in the 35th minute. Friedel punched a cross away, but only to an unmarked Blanco in the middle of the area where his shot was denied by the American goalkeeper.
Braulio Luna tested Friedel with an accurate free kick in the second half. Luna bent one from wide right which Friedel pushed into his own crossbar and over the net.
On the ensuing corner kick, John O'Brien used his hand to prevent the ball from reaching Blanco's head. That went unnoticed by referee Vitor Melo Pereira of Portugal.
"A U.S. player hit the ball with his hand and everyone saw it on the big screen, but the referee didn't catch it," Mexico coach Javier Aguirre said.
Pereira issued five yellow cards to each team and sent off Mexico's Rafael Marquez for an aerial head-on-head challenge on Cobi Jones.
"It's a rivalry, we know each other and there's been a lot of bad blood over the years, but when the game is over, we're friends again," said Arena.
Arena used a wise strategy against their known neighbours south of the border. Reyna played well on a defensive role, while Gregg Berhalter and Pablo Mastroeni clogged the middle of the backline.
"Reyna played a position he was not used to, and he came through big," said Arena, who also started Lewis and Wolff. "I felt Eddie Lewis' time has come. And Gregg Berhalter, Josh Wolff were ready to go. I thought we needed some fresh legs in here today. It's been a difficult tournament with a number of games played in a short period."
It was by far a better American performance than the group finale against a robust Poland in which the U.S. were caught flat-footed.
Germany beat the Americans in a friendly on March 27 in Rostock, 4-2. The teams also met in the 1998 World Cup, with the Germans winning 2-0 in group play.
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