A week after it thrashed United States 104-14 in Washington, New Zealand found greater resistance in the Welsh capital, but eventually took the game away from its host, turning a spicy Autumn Nations Series contest into a drubbing.
Barrett took New Zealand beyond 50 points in the 79th minute with his second try of the match, and the visitors' seventh in total.
New Zealand raced into a fourth-minute lead, centurion Barrett intercepting a pass from Gareth Anscombe and charging through to score under the posts.
Try scorer Barrett was spared a yellow card after a seemingly deliberate knock-on, before Wales lost Alun Wyn Jones to injury on the day the captain beat Richie McCaw's record tally of 148 caps for an international team. Jones suffered the upper-body blow when tackling Jordie Barrett.
New Zealand was well on top and had a second try in the 34th minute when scrum half TJ Perenara scuttled in from close range. Prop Nepo Laulala was then only shown a yellow card after making heavy contact with the head of Ross Moriarty in a tackle, perhaps a let-off for the tourists.
Kicking from Anscombe, Jordie Barrett and Rhys Priestland kept the scoreboard ticking along, before wing Will Jordan produced a thrilling third All Blacks try, chipping ahead and sprinting through to collect and dot down.
Johnny Williams thrilled the home crowd when he threw himself on Priestland's skidding kick behind the All Blacks defence, narrowing the gap to 28-16.
Then came the New Zealand surge, as Dalton Papalii exploited a gap in the Wales defence from a lineout to inflict more punishment, Sevu Reece exchanged passes on the left with Ardie Savea before dashing in, and Anton Lienert-Brown raced to the corner on the opposite flank.
Beauden Barrett had the final say, another interception seeing him gain possession on halfway, reading the pass from Johnny McNicholl and driving to the line.