Manchester United defender Gabriel Heinze broke the deadlock just before the break and Lionel Messi doubled the lead on the hour mark with a brilliant effort.
Villarreal-bound playmaker Juan Roman Riquelme completed the rout from the spot five minutes later.
Argentina, who are looking for an unprecedented 15th Copa America title, face old rivals Brazil in the competition's final on Sunday.
Heinze opened the score line one minutes before the interval when he volleyed home Riquelme's free-kick at the back post.
Barcelona sensations Messi added the second in the 60th minute when he received Carlos Tevez's pass in the right-hand side of the area before sending a superb chip over the advancing keeper.
Riquelme killed off Mexico's hopes in the 65th after successfully converting a penalty that was awarded to Argentina following Rafael Marquez's obstruction to Tevez.