Muhammad Imran converted a penalty corner in the 30th minute to give 1-0 lead to green shirts.
Veteran penalty corner specialist Sohail Abbas scored second goal in the 44th minute of the game for Pakistan.
Argentina got few chances on penalty corner just after the start of the second half but had them saved by Pakistan’s goalkeeper Imran Shah.
Pakistan will play their third Olympic match against Britain on Friday at 8pm PST.
Pakistan began their Olympic campaign with a 1-1 draw against Spain.