Argentina produced a committed defensive onslaught early on against Wales but in the fifth minute James Davies touched down to give Will Thomas the opportunity to knock over the extras. The Cardiff full back slotted the conversion and then quickly added a converted try himself to put Wales 14-0 up at the break.
Juan Ignacio Brex scored midway through the second half for Argentina. Gaston Revol added the conversion but Wales were able to hold out for an invaluable win.
Wales claimed their spot in the Cup Quarter Finals with a clash against Samoa with a commanding 22-5 win over Russia in their final match with captain Shellard crossing for a well taken hat trick.
But the group belonged to New Zealand who remained unbeaten on Day One with wins over Wales, Russia and Argentina (17-7) in their final match.
New Zealand were one of only three undefeated teams on Day One, along with Canada and Fiji, and they will face giant killers Portugal in the Cup Quarter Finals while Wales will face Samoa in the Cup Quarters.
Russia will go through to the Bowl tomorrow where they face a tough assignment against South Africa while Argentina also have a tough match against England in their Bowl Quarter Final.