Captain McCaw scored the first try of the game after 20 minutes, before Ma'a Nonu touched down on the stroke of half-time to give New Zealand an 18-6 lead.
Two more tries shortly after the break from Charles Piutau and Kieran Read, both converted by Carter, put New Zealand further ahead, before Agustin Creevy finished two pushover tries to pull Argentina back into the contest at 31-18.
However, unbeaten at the AMI Stadium since 1998, the All Blacks refused to budge, and replacement hooker Codie Taylor sealed the win with a debut try with ten minutes left.
McCaw said: "There was a wee patch in the second half where our discipline let us down and they got a few tries through drives on the back of us giving away a few penalties.
"We upped the intensity which we needed to do from last week. We aren't quite there yet but it's a step.
"Personally, today was a step, still not perfect, but it never is, and I was happy with some parts.
"Being a bit relaxed and enjoying running around means you get stuck in doing the job for the team, which is what it's all about."
The following day in Brisbane, Australia came from 20-10 down with seven minutes left to beat South Africa thanks to a try after the clock had gone dead from Tevita Kuridrani.
Tries either side of half-time from Eben Etzebeth and Jesse Kriel had put the Springboks ahead, but a Michael Hooper try triggered a comeback to give the Wallabies a crucial 24-20 win.
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