The Scots scored three tries, with Tim Visser scoring a try in each half and prop Geoff Cross also going over.
All Blacks superstar Carter booted 21 points and pulled the strings in attack as Julian Savea (two), Israel Dagg, Corey Jane, Andrew Hore and Ben Smith all scored tries.
"I'm very happy. We wanted to get this tour off to a good start and we were up against a Scotland side full of energy and intensity and they really took it to us, so I'm really pleased to get off on the right foot," he said.
"It was pleasing for us to score a few tries but there are still a few areas to work on. For periods of the game, especially the second half, Scotland really took it to us and controlled the territory.
"We were a bit passive at times. Scotland played with a lot of passion, they were extremely physical and scored some good tries."
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