Winger Panetta struck first in the 25th minute after getting on the end of a well-worked free kick.
Panetta then doubled the lead in the 52nd minute with an audacious volley from 25 yards that eluded everyone and the Argentine keeper.
Argentina piled on the pressure late in the second half, with captain Tomas Conechny converting from the spot in the 67th minute after Charlie Devereux was adjudged to have clipped substitute Lucas Pizzatti in the box.
And Argentina almost drew level shortly after, when a solid move was capped off with a header, but was chalked off as off-side.
Australia held on to finish the group third on four points and will only know if it will face Nigeria or Korea Republic in the Round of 16 after tomorrow's final group games are completed.
Germany 1-2 Mexico
Mali 3-0 Honduras
Ecuador 2-0 Belgium