The All Blacks were always confident of victory against the Pumas despite an error-riddled performance that saw them pushed right to the end.
Two late tries eventually put the result beyond doubt with New Zealand, who were playing at home in Wellington, winning the Rugby Championship Test 21-5.
But the message at half-time, when the lead was a mere 6-5, was "just keep plugging away and eventually they'd crack and that's how it turned out", centre Conrad Smith said.
The win kept unbeaten New Zealand at the head of the table after the third round while Australia's 26-19 win over South Africa lifted them off the bottom of the ladder and ahead of Argentina who have a sole draw after three games.
In a match played in swirling wind and rainy conditions, Aaron Cruden kicked three penalties for the All Blacks with tries to wingers Julian Savea and Cory Jane while prop Rodrigo Roncero scored for Argentina.
Although the All Blacks never doubted their ability to win they were also impressed with the performance of the Pumas in their first year in the southern hemisphere championship and who drew with South Africa 16-16 two weeks ago.
"They're a welcome addition to this competition," coach Steve Hansen said.
"They're only going to get better and better and they're a very good side at the moment, probably one of the best defensive teams in the world."
But Hansen added that despite a high error count, dropped passes and inaccurate decision making, "In reality the game was well and truly in our control most of that second half".
"Our forward pack showed us they're capable of fronting it with a very physical side, our line-out was very good both on attack and defence and we disrupted a lot of Argentinian lineout ball," he said.
The Pumas lost seven of 19 line-outs on their own throw but had the beating of the All Blacks in the scrums where they won three strikes against the head and lost one.
Smith, who missed the first two Rugby Championship matches because of an eye injury said the physical, bruising approach of the Argentinians was what they expected but they still struggled to adapt to it.
"That's maybe why we took a while to build a lead. We're aware we're still not playing as good as we'd like so I'd be more concerned if we were really happy," he said.
"We know we can play a lot better and thankfully there's a lot of Tests for us left in the year to try and do that."
In fourth-round matches next weekend the All Blacks play the Springboks in Dunedin while Argentina play Australia on the Gold Coast.