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Najar almost found an equaliser on the stroke of half time, as he smashed a shot marginally over the crossbar, but USA doubled their lead after the break.
Michael Bradley whipped in a free kick, and Dempsey headed the ball into the back of the net from a few yards out.
Honduras did hit back a few minutes later through Carlos Discua, who burst forward and slammed the ball past Guzan, but they failed to find an equaliser and so start the tournament with a defeat.
USA go top of the group, which also contains Panama and Haiti.