Johnson's header off a Landon Donovan corner kick put the U.S. ahead for good and Donovan added an insurance tally from in close in the 78th for the Americans, who won their 26th straight home-field qualifier.
Clint Dempsey could have made it 3-0 but missed a penalty kick in the final second.
The victory put the U.S. squad at the doorstep for a berth in the 2014 World Cup.
Fourth-place Mexico, meanwhile, dropped its second straight qualification match.
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