Ireland led for the entire 80 minutes at the new Aviva Stadium, with a win over the Pumas never looking in doubt in freezing conditions in the Irish capital.
A Stephen Ferris try and some impressive goal kicking form Jonathan Sexton gave Ireland a 19-3 lead at half-time and the visitors never threatened to overturn that substantial deficit.
Gordon D'Arcy added a second try in injury time after fellow Lion Keith Earls had seen the television match official rule out his own score just moments earlier.
Sexton finished with 17 points in total courtesy of five penalties and a conversion, while triple Lions tourist Ronan O'Gara added the extras to D'Arcy's late effort.
The 29-9 result was Ireland's biggest-ever over Argentina and ensured they ended the autumn series with two wins from four games, as they bounced back from last weekend's defeat to New Zealand.
Scotland also ended their November campaign with two wins after they backed up an historic triumph over South Africa with a last-gasp victory over Samoa in Aberdeen.
Replacement fly-half Ruaridh Jackson was the hero for the Scots at Pittodrie, with the Glasgow Warriors youngster slotting an 80th-minute penalty to seal a 19-16 win.
Andy Robinson's men went into Saturday's fixture holding their highest-ever position in the IRB World Rankings but it looked as though would have to settle for a draw against an impressive Samoa.
Ospreys wing Nikki Walker scored Scotland's only try, while Dan Parks kicked 11 points before Jackson's late introduction.
The result was Scotland's fifth win in six games, with their only recent blemish coming against the All Blacks a fortnight ago.
Wales couldn't match their Celtic cousins, however, as they slipped to a 37-25 defeat at the hands of New Zealand in Cardiff on Saturday night.
Warren Gatland's men were always within striking distance until a late surge from the All Blacks saw them score two tries in the final eight minutes to put the result beyond doubt.
Lions full back Lee Byrne scored a consolation try for Wales at the death, while fellow Lions tourist Stephen Jones jumped to seventh in the list of leading points scorers in international rugby thanks to a 20-point haul.