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Dempsey scored his 51st international goal in the 27th minute, but the Americans' defense was upended just three minutes into the second half.
Yedlin got his first yellow in the 47th for a slide tackle from the side into Miguel Almiron near the center circle and then when play resumed raised a foot and charged into Miguel Samudio near a sideline. Chilean referee Julio Bascunan immediately gave a second yellow, and Yedlin lifted both arms wide as if to say, why me?
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Michael Orozco entered to play right back in the 50th, and Dempsey came off as the U.S. prepared to survive an onslaught. With Paraguay applying pressure, U.S. coach Jurgen Klinsmann repeatedly turned to try to spur on the crowd of 51,041.
American goalkeeper Brad Guzan made an outstanding body stop on a short-range shot in the 82nd minute, then made a kick save on an attempt off the rebound. Gustavo Gomez put the ball past Guzan in the 89th but whistled for offside.
Hosting a special 100th anniversary of South America's championship, the U.S. (2-1) will finish first or second in Group A depending on the result of Colombia's match against Costa Rica later Saturday and will play a quarterfinal against Brazil, Peru or Ecuador at Seattle or East Rutherford, New Jersey. Colombia also clinched a knockout stage berth.
Paraguay (0-2-1), which lost to Argentina in the semifinals of last year's Copa America, was eliminated.
For more on the COPA America competition including stats and scores, click here.