It was only a third-ever win for the Pumas over New Zealand in 38 meetings as the adventurous spirit of the Argentines prevailed against a ragged-looking All Blacks, who were uncharacteristically error-prone.
The lead changed several times before Argentina prevailed in an exciting encounter that was in stark contrast to New Zealand's one-sided 44-6 win over the Pumas when they last met in the World Cup semi-final in Paris last October.
Argentina's tries came from Lucio Cinti, Mateo Carreras, Franco Molina and a poignantly decisive try for the 39-year-old Agustin Creevy.
Santiago Carerras kicked a vital 18 points with four penalties and three conversions.
New Zealand's tries came from Sam Darry, Anton Lienert-Brown and Mark Tele'a with Damian McKenzie putting over three penalties and three tries.
It was a typical piece of All Black ingenuity that saw the home side go over for the first try in the 15th minute as McKenzie chipped ahead in his own half, regained the ball before feeding out to Beauden Barrett, who kicked in-field for a chase that ended with a try for lock Darry.
Argentina stripped possession in the maul to set up their opening try eight minutes later, with captain Pablo Matera drifting across the line before popping a short pass up for Santiago Chocobares to burst through before Cinti finished off.
Lienert-Brown went over at the end of a line out drive in the 35th minute but two minutes later Sevu Reece's tap back off a high ball sat up perfectly for Mateo Carreras to grab possession and speed over for a second Argentina try that brought the halftime score to 20-15.
The visitors went ahead three minutes into the second half with a try from Molina from a clever line out routine and Carreras converted to put Argentina 22-20 ahead.
The All Blacks' third try came in the 52nd minute as winger Tele'a slipped through and score under the posts.
New Zealand mistakes set up Argentina's fourth try, with two wayward passes from Asafo Aumua and McKenzie leading to Rieko Ioane having to dot down behind his own line. From the resultant five-metre scrum, Argentina set up a score for Creevy and went 35-30 up with 10 minutes left.
Argentina secured the win two minutes from the end with a Carreras penalty after the Kiwis were blown up for slowing down play.
New Zealand host Argentina again next week at Eden Park in Auckland.
