The All Blacks raced into a 17-0 half-time lead but Scotland fought back to level with 20 minutes to play and give the home crowd hope, only for Damian McKenzie to snatch victory for the visitors with an extraordinary try before adding a penalty two minutes from time.
Cam Roigard and Will Jordan scored the other All Blacks tries while Beauden Barrett booted over seven points with a penalty and two conversions.
Scotland's tries came from Ewen Ashman and Kyle Steyn while Finn Russell kicked seven points.
Scotland had hopes of a historic triumph as Murrayfield celebrated a century since hosting its first Test, but the crowd were stunned into silence in the third minute as lock Josh Lord broke from a midfield maul and burst towards the try line before offloading for Roigard to score.
Scotland needed desperate defending to keep from conceding again with wave after wave of attack in the middle of the first half but the sustained pressure did allow Beauden Barrett put over a penalty to increase the score to 10-0.
In a quick break down the short side, Wallace Sititi easily shrugged aside Darcy Graham as Scotland's defence looked to go to sleep, and Jordan scored on the stroke of halftime to put New Zealand well in command.
Scotland's first try came six minutes into the second half as Ashman went over from a line-out maul after which visiting skipper Ardie Savea was sent to the sin bin.
Five minutes later Scotland scored again when captain Sione Tuipulotu sucked in the defenders, allowing Blair Kinghorn to swing out a long pass out for Steyn to go over in the corner.
Russell's penalty on the hour mark brought Scotland level, however, after McKenzie was caught offside.
The Kiwi substitute redeemed himself, however, with eight minutes left as he held off two tacklers to dot down, keeping his feet infield and twisting his body to score.
McKenzie slotted over an insurance penalty two minutes from the end to ensure an escape for New Zealand, who kept up their bid for a Grand Slam with England and Wales next on their after beating Ireland in Chicago last week.
New Zealand have now won 31 of 33 tests against the Scots since their first clash in Edinburgh in 1905, with two draws.
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