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.
Kelly Brown won his 50th cap and first as captain as Scotland went in search of a first victory over world champions New Zealand in the EMC Test at Murrayfield.
Number eight Brown was included as one of five changes from Scotland's previous outing, the June 23 win in Samoa, with Jim Hamilton returning at lock alongside Richie Gray, who proved his fitness following an ankle injury.
New Zealand, unbeaten in 17 Tests, fielded a team showing 10 changes from the draw with Australia, but included captain Richie McCaw at openside flanker and fly-half Dan Carter.
When the All Blacks last played in Edinburgh, confidence among the hosts was high, but Scotland were beaten 49-3.
Murrayfield's famous pre-match welcome included a parade by Scotland's Olympians and Paralympians, a match-ball presentation by cyclist Sir Chris Hoy and a statement of intent from the hosts, who walked towards the Haka.
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.
Tighthead prop Geoff Cross conceded another penalty for collapsing a scrum, but unusually Carter's effort was short and off target.
Carter's afternoon soon worsened when his pass was intercepted by Matt Scott at the halfway line and the centre popped the ball to supporting wing Tim Visser, who touched down on his Murrayfield debut.
It was Scotland's first try against the All Blacks in four Tests, since Simon Webster's score in 2005. Greig Laidlaw converted.
The visitors responded swiftly though, as Carter's midfield break was the spark for Israel Dagg to go over on the right as New Zealand reclaimed the lead with ease.
Rennie was injured in the build-up and went off nursing a shoulder injury, with David Denton coming on, and Carter kicked the conversion to put the All Blacks 10-7 in front.
Cross ignored an overlap in the Scotland back-line, but the hosts won a penalty for an indiscretion on the floor by New Zealand and Laidlaw levelled the scores from in front of the posts.
Dagg clashed heads with Sean Lamont and went off for Beauden Barrett before Scott was penalised for not rolling away from the tackle, allowing Carter to restore his side's three-point lead.
Just a few moments later, New Zealand stretched Scotland from one wing to the other, making space for Julian Savea to breeze by Visser and score in the left corner. Carter converted.
A poor kick-off then gifted the ball back to New Zealand and Wyatt Crockett punched a hole through the home defence to create an overlap which allowed Corey Jane to score in the right corner. Carter again converted.
The direct route was next, with hooker Andrew Hore rolling out of an attempted Cross tackle to dot down on the right. Again Carter's kick was successful.
Scotland finished the half on the attack with a tap-and-go penalty in stoppage time.
Denton bounced out of a McCaw tackle, Lamont was stopped short of the line and then Scott went over, but the television match official ruled Piri Weepu held him up.
Another penalty followed, Gray twice going close, before Cross bundled over for his first Test try which Laidlaw converted.
Scotland were granted a numerical advantage for 10 minutes early in the second half when Adam Thomson was shown a yellow card for stamping on the head of Alasdair Strokosch at a ruck.
Replays suggested Thomson's punishment might have been more severe than 10 minutes in the sin-bin and he is likely to be cited for further action.
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.
Scotland kept the pressure on the world champions, but could not find a further way through the stern defence.
Despite toiling in their own half for much of the third quarter, New Zealand quickly responded after a poor Ford lineout throw resulted in an All Blacks scrum.
Carter chipped to the left where Savea gathered and scorched past 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.