Mexico was able to complicate La Albiceleste and never looked in danger of losing their lead throghout the game.
In the 10th minute, Chivas striker Kevin Magana showed his quality when he dribbled past two defenders and put a well placed shot past Hernan Peano to give Mexico the lead.
El Tri then gave the initiative to the Argentines, who failed to break through an orderly Mexican defense.
Mexico earned a penalty in the 76th minute, and Francisco Venegas stepped up to seal the points and start the tournament on the right foot for El Tri.
With the result, Mexico moved up to second in Group C and will face Australia next on Wednesday.