Flanker Dalton Papali'i opened the scoring for New Zealand after just four minutes, appearing to read an English strike play off the tail of their lineout and intercepting Jack van Poortvliet's pass to run 45 metres untouched.
They added a second minutes later, Codie Taylor bundling over from a lineout after England were penalised at the scrum, and the hosts were in bad shape at 0-14 down inside 10 minutes.
Scrum half Van Poortvliet, whom many England fans wish Eddie Jones would start more often over the veteran Ben Youngs, endured a torrid start to the game with his intercept pass being followed by a sacking off the base of a scrum.
That nearly cost England a third try before it was disallowed, but worse was to follow.
The Twickenham crowd had been revved up by pregame footage on the big screens of England's best performance under Jones and the last time these sides met, the 2019 World Cup semi-final where the men in white were unstoppable.
How distant a memory that soon seemed.
Where in 2019 back-rowers like Tom Curry and Sam Underhill perfected a brutally front-foot defence as England stunned the All Blacks into submission, on Saturday New Zealand repeatedly sidestepped the rush defence to find gaps.
They found joy all day with kick-passes too, wingers Jonny May and Jack Nowell spending much of the day scrambling across the turf to try and put out fires.
The sides exchanged penalties either side of the break as England fought for a foothold in the game, and the fractious crowd's mood darkened further when Rieko Ioane scorched down the left wing to make it 6-22.
With seemingly nothing to lose, England exploded out of nowhere, Marcus Smith skipping through a gap to set up a close range Stuart try and Freddie Steward rounding off a free-flowing attack to add another.
The Twickenham crowd were delirious when Stuart went over again in the final minute, with Smith converting to complete a remarkable comeback.
After the buzz fades some fans may query why England did not push for the win given how rampant they were at the close, Marcus Smith opting to kick it out and settle for a tie that had seemed impossible for the first 70-odd minutes.
"I think it depended where we had the ball. It's a difficult place to go from. They had bodies piling in, we had men out. It was the right decision I think," Owen Farrell said.
Neither side has been at its best in this Autumn series, with England suffering a dispiriting loss to Argentina before thumping an unusually meek Japan last week while New Zealand's bench helped them come from behind against Scotland.
England next face South Africa, their nemesis in the 2019 World Cup final, although they can look to their last-gasp win over the Springboks in the 2021 round of Autumn fixtures for some inspiration against an intimidating-looking lineup.
New Zealand meanwhile return home unbeaten at least, and can spend the flight wondering how they threw away such a commanding lead as they turn to preparation for next year's World Cup.
