Visser scored a try in each half and Geoff Cross also went over for the hosts, for whom Greig Laidlaw kicked seven points, but the All Blacks ruthlessly punished any mistakes.
Julian Savea (two), Israel Dagg, Corey Jane, Andrew Hore and Ben Smith crossed for the All Blacks, with Dan Carter kicking 21 points.
The one blot on the tourists' record came when Adam Thomson was sin-binned for stamping on Alasdair Strokosch's head.
Scotland had not scored a try against New Zealand since 2005 and they scored three for the first time since 1996, two for a Holland-born Edinburgh wing who qualified through residency in June.
Visser's 14th-minute score put Scotland in front, but three converted tries in a 10-minute spell turned the contest in the All Blacks' favour and Andy Robinson's men will now seek to bounce back against South Africa and Tonga.
New Zealand, meanwhile, resumed winning ways after a draw against Australia in their prior Test saw them miss a record-equalling 17th successive Test win.
Now the All Blacks face Italy, Wales and England as they bid to finish the calendar year unbeaten.
Hopes were high in 2010 of a Scotland upset, only for the hosts to lose 49-3, and two years on ahead of the 29th Test between the sides, Scottish expectation was tempered in the build-up, despite summer successes in Australia, Fiji and Samoa.
Murrayfield's famous pre-match welcome included a parade by Scotland's Olympians and Paralympians as well as a match-ball presentation by cyclist Sir Chris Hoy.
There was also a statement of intent from the hosts, who walked towards the Haka, led by Kelly Brown on his 50th Test and first as captain.
But in the opening minute the pressure was released as Scotland openside flanker Ross Rennie was penalised for hands in the ruck and Carter kicked over the resulting penalty.
Carter missed a penalty kick before his pass was intercepted by Matt Scott at the halfway line.
The centre popped the ball to supporting wing Visser, who touched down on his Murrayfield debut. Laidlaw converted.
New Zealand reclaimed the lead with ease, with Carter's midfield break the spark. Dagg went over on the right and Carter converted.
Scotland suffered a further blow as Rennie went off with a shoulder injury, with David Denton coming on, before Laidlaw and Carter exchanged penalties.
New Zealand then elected to raise the tempo and scored three times in quick succession to take a commanding lead.
First, Scotland were stretched from one wing to the other and Savea breezed by Visser to score in the left corner.
A poor kick-off gifted the ball back to New Zealand and Wyatt Crockett punched a hole through the Scotland defence to create an overlap which allowed Jane to score in the right corner.
The direct route was next, with hooker Hore rolling out of an attempted Cross tackle to dot down on the right. Carter kicked his fourth conversion of the match, but there was still time for a Scotland response before the half-time whistle.
They laid siege on the All Blacks line. Denton bounced out of a McCaw tackle, Sean Lamont was stopped short of the line and then the television match official ruled against Scott.
Another penalty followed, though, and Richie Gray twice went close before Cross bundled over for his first Test try. Laidlaw converted.
Scotland had a numerical advantage for 10 minutes early in the second half when Thomson trod on Strokosch's head at a ruck. Replays suggested Thomson's punishment might have been more severe than 10 minutes in the sin-bin.
A succession of lineouts followed, but Brown was unable to gather Ross Ford's throw, allowing the All Blacks to clear.
Scotland surged back, but loose play saw the ball in All Black possession once more, only for the tourists to uncharacteristically lose it at the breakdown.
Centre Tamati Ellison was tackled and Laidlaw stepped over to kick the ball through for Mike Blair to scoop it up. Blair in turn fed Visser for the wing to claim his second try of the afternoon.
Despite toiling in their own half for much of the third quarter, New Zealand then scored a fifth try.
Carter chipped to the left where Savea gathered and scorched past Stuart Hogg for his second try of the game.
Numerous changes ensued, with Glasgow Warriors scrum-half Henry Pyrgos among them to make his debut, before a flat conclusion to the contest was enlivened by the tourists' sixth try.
Scotland substitute Max Evans missed a tackle on Carter and Ben Smith was able to go over in the corner. Carter converted to complete a handsome victory.