U.S. forward Clint Dempsey converted a low cross from Gyasi Zardes in the 27th minute as the hosts had the better of the early exchanges.
However, the Americans were reduced to 10 men shortly after half-time when right back DeAndre Yedlin received two yellow cards within a minute for aggressive tackles.
“The boys showed a lot of heart, especially after that red card,” Dempsey said. “Man, we showed a lot of character and we’re proud to advance to the next round.”
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The United States looked set to fall behind in the 11th minute when Paraguay had a three-on-one break but defender John Brooks chased down Miguel Almiron to deliver a terrific sliding challenge and knock the ball out of play.
Goalkeeper Brad Guzan, who made key saves from Jorge Benitez and Almiron in the 82nd minute, paid tribute to his defence.
"The guys in front of me were fantastic,” said Guzan. “Every now and then it’s up to the goalkeeper to come up with the save and I was lucky enough to do that tonight.”
In the later Group A game, Costa Rica’s Johan Venegas scored in the second minute before Frank Fabra pulled Colombia level four minutes later.
Fabra turned villain in the 34th minute by scoring an own goal and Celso Borges put the Costa Ricans 3-1 up just before the hour mark.
Colombia’s Marlos Moreno made it 3-2 with 17 minutes left but they could not find the equaliser.
(Reporting by Tim Wharnsby; Editing by Peter Rutherford)
