On a national team level, never. However, on U-17 and U-20 tournaments (players under ages of 17 and 20, respectively) Mexico has won over Brazil on various times:
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During the FIFA Confederations Cup. The match was held in June 19, 2013. Mexico lost 0-2 versus Brazil.
El Salvador last beat Mexico on April 4, 2007 by a goal difference of 2-1 in El Salvador.
Brazil beat Italy in the final 4-1In 1970 Brazil beat Italy 4-1 in the final of the World Cup.
Brazil won their last World Cup in 2002, beating Germany in the final.
Yes, Argentina are better than Mexico. Argentina put Mexico out in the last World Cup.