Wales were first to cross the whitewash as full-back Hallam Amos' superb offload out the back door sent Scarlets flanker James Davies clear, as he dotted down for his first Test try, while George North powered through to score his 33rd touch down after Gareth Davies sprinted clear.
Fly-half Rhys Patchell kicked 10 points to keep Wales in the driving seat.
Argentina had chances to score but were denied by last-ditch Welsh defence, notably by Ross Moriarty, Elliot Dee and captain Hill, so had to settle for Tomas Lezana's late consolation try.
The match also saw Aaron Wainwright make his international debut for Wales
Next week there's the re-match at Santa Fe.
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