Ewan Ashman gave Scotland hope of a first win over New Zealand by scoring a hat-trick in an extraordinary first half featuring seven tries in total that ended with the All Blacks only narrowly in front at 24-21.
But improved New Zealand discipline and ball retention enabled them to pull clear with three tries after the interval, while they denied Scotland a score in the second half.
It was an all-too-familiar tale for Scotland, in their first match of the season, as they succumbed to a New Zealand side fresh from two wins over Australia.
Full-back Barrett's second try of the match meant he joined Will Jordan in notching 50 Test tries for the All Blacks.
Victory gave New Zealand a 32nd win in 34 Tests against Scotland, with two draws, dating back to 1905.
It also meant the All Blacks remained unbeaten in the inaugural Nations Championship following a trio of wins in the southern hemisphere-based section in July.
Scotland ran New Zealand close in a 25-17 defeat at Murrayfield last year.
But it took New Zealand a mere three minutes to open the scoring on Saturday, when a clever line-out move ended with No. 8 Wallace Sititi powering over for a try that Damian McKenzie could not convert.
Scotland, however, were ahead just five minutes later when hooker Ashman was driven over from a close-range line-out. Finn Russell added the extras, and Scotland led 7-5.
But New Zealand soon led 17-7 after scoring two tries in quick succession through forwards Ethan de Groot and Codie Taylor.
The All Blacks, however, were reduced to 14 men after flanker Peter Lakai was shown a yellow card.
Scotland capitalised when Ashman went over for his second try with a powerful carry after a neat tip-on from Scotland captain Sione Tuipulotu.
Russell's conversion reduced New Zealand's lead to three points.
Yet despite being a man down, it was the All Blacks who scored next when, after from an overlap, Barrett picked an excellent line to secure a four-try bonus point as early as the 31st minute.
McKenzie's successful conversion meant the All Blacks were again 10 points ahead at 24-14.
But just as Lakai's spell in the sin-bin was ending, Sititi was shown a yellow card.
New Zealand defended ferociously to deny Scotland, but their line was breached again when Ashman completed his hat-trick - the first by a Scot against the All Blacks - as he finished off another driving maul, with Russell landing the conversion.
Following such a breathless first half, the pace understandably slowed.
But after another dominant scrum, New Zealand went wide to Josh Moorby, with the wing finishing in the corner.
And with centre Tuipulotu in the sin-bin after persistent infringements by Scotland, Barrett was left free and clear to score his second try.
New Zealand replacement hooker Asafo Aumua set the seal on victory 13 minutes from time with the All Blacks' seventh try as he rounded off a fine line-out move.