In front of a crowd of 84,519 in Texas, El Tri ended Brazil's 10 match unbeaten run with two first half goals to give themselves a major confidence boost ahead of World Cup qualifying fixtures this weekend.
Dos Santos gave Mexico the lead in the 22nd minute in fine style with a lob from the left that surprised Brazil goalkeeper Rafael and went into the top right corner.
The striker then won his side a penalty after being brought down by Juan in the box, with Javier Hernandez converting the spot kick.
Sandro also completed the full 90 minutes as Brazil's preparations for the Olympics in London took a minor setback.
In Rustenburg, Ethiopia held South Africa to a surprise 1-1 draw.
Steven Pienaar and Bongani Khumalo both played the whole match as Bafana Bafana needed a late goal to secure a point in their opening 2014 World Cup qualifying game.
South Africa next face Botswana in their second Group A fixture in Gaborone on Saturday.