The All Blacks had to come from 17-0 down to beat Australia in their last match and they were given another scare by the winless Pumas, who held a 22-15 second-half advantage.
Nehe Milner-Skudder and Anton Lienert-Brown scored early tries for New Zealand but six points from the boot of Nicolas Sanchez and a huge penalty from Emiliano Boffelli kept the visitors in touch.
Israel Dagg went over out wide just before the break to extend the home side’s lead only for Sanchez to touch down on the last play of the half.
The Irish Times reports Beauden Barrett’s three missed conversions allowed Sanchez to nudge Argentina ahead at half-time and another Boffelli penalty just after the restart gave them a 19-15 lead.
Everything appeared to be going Argentina’s way when Barrett was sin-binned and Sanchez put them seven points clear, but the 14-man All Blacks drew level through Vaea Fifita’s converted score.
The game was still in the balance with 20 minutes remaining but tries from Damian McKenzie and Barrett either side of a Lima Sopoaga penalty gave New Zealand a third straight win.