The 20-year-old Stanford University student opened the scoring when he pounced on a loose ball and fired a right-footed shot past the Mexican keeper from about 10 yards in the 49th minute at a sold-out Alamodome crowd of 64,369.
Morris, a Seattle native who has yet to play a professional game, is the first college player to appear for the U.S. in two decades. He was substituted in the 65th minute.
Juan Agudelo added a second American goal with a fierce shot from just outside the box in the 72nd minute.
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Mexico created few chances in a match played on an uneven surface which detracted from the quality of the spectacle.
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