Up 17-0 after a dominant first half, New Zealand lost control in the third quarter as the inspired home side brought Murrayfield to life and levelled the score.
Super-sub McKenzie entered the contest early in the second spell in place of an injured Caleb Clarke but his biggest impact came late in the contest when the result was in the balance.
The Chiefs playmaker contorted his body and planted the ball over his shoulder in the corner to break the deadlock.
Then with time ticking, McKenzie slotted a challenging penalty shot from 45m out to make the result safe and ensure the All Blacks retained their historic unbeaten record against the Scots - a mark that stretches back 33 matches over the 120 years.
New Zealand are halfway towards their Grand Slam tour goal after opening with victory over Ireland in Chicago last week.
Matches remain against England at Twickenham next week, followed by Wales in Cardiff.
The record against Scotland appeared in jeopardy as the home side came to life soon after the break, scoring tries through hooker Ewan Ashman and winger Kyle Steyn.
Both tries were converted by first-five Finn Russell and his penalty in the 60th minute drew the teams level.
It was major momentum swing after an early try to halfback Cam Roigard gave the All Blacks control before Will Jordan crossed soon before the interval. Both tries were converted by first-five Beauden Barrett, who also landed a penalty.
Roigard's try was set up by a brilliant 40m run and offload from lock Josh Lord, who spotted a gap at the base of a ruck.
Jordan's try came from slick skills down the blindside from flanker Wallace Sititi, who was arguably the visitors' best during their dominant first spell.
New Zealand's cause wasn't helped by yellow cards shown to winger Leroy Carer, captain Ardie Savea and Sititi during the middle period of the game.
That lack of discipline helped Scotland back into the contest, only for New Zealand to finish the stronger side for the second time in two weeks.
