El Tri begun in assured fashion, with Raul Jimenez hitting the woodwork seconds into the match and Marco Fabian missing a key opportunity moments later.
The hosts were then effectively the better side throughout the rest of the game and came close to taking the lead when Lautaro Martinez forced a brilliant save from Guillermo Ochoa in the 38th minute.
Argentine took the lead just before the half when a miscommunication off a free-kick allowed Ramiro Funes Mori to head in the go-ahead goal.
Tuca tried to lead a rally at the break by making a number of significant substitutions, but in truth, el Try never really threatened again.
In the 83rd minute, Argentina put the game away when a cross from the right-wing side finished with Isaac Brizuela putting the ball into the back of his own net.
Mexico and Argentina are set to meet again in four days in the city of Mendoza.