In matches played between the two countries in Mexico, the United States now has a 1-23-1 record.
The Mexican national team lost in Azteca Stadium for only the ninth time in 120 matches.
Javier Hernandez missed a chance to put Mexico ahead in the 76th minute when his header from close range sailed wide of the post.
Orozco then made Mexico pay by scoring the winning goal soon after entering the match.
U.S. goaltender Tim Howard made two spectacular saves late in the exhibition contest to preserve the win.