The win extends England's unbeaten run to 10 games.
The pre-match favourites overturned an early deficit to secure their 10th consecutive win under head coach Steve Borthwick.
George Ford played a central role in the victory, guiding England back from 12-0 down with two drop goals late in the first half.
The fly-half, who missed a decisive drop goal in the same fixture last year, was influential throughout as England claimed their first win over the All Blacks since the 2019 World Cup.
New Zealand struck twice in three minutes during the opening quarter through Leicester Fainga’anuku and Codie Taylor, as England’s wide defence was exposed.
Freddie Steward departed with a head injury to usher Marcus Smith on to the field and the full-back was soon involved as Earl launched a counter-attack that ended with Feyi-Waboso being stopped close to the line.
But England responded after a strong period of pressure, with Ollie Lawrence powering over from a scrum move in the 25th minute.
Two quick drop-goals by Ford reduced the deficit to one point at half-time, and England took control early in the second half after Taylor was sent to the sin bin for handling on the floor.
Sam Underhill crossed in the 44th minute to give the hosts the lead for the first time, and a well-executed line-out move allowed Fraser Dingwall to extend the advantage 10 minutes later.
New Zealand briefly threatened a comeback when Will Jordan scored while Ben Earl was in the sin bin, but England regained composure.
A Ford penalty and Tom Roebuck try confirmed England’s first win over the All Blacks at Twickenham since 2012.
Scrum-half Alex Mitchell said afterwards: "I feel fantastic, the crowd felt extra loud today, and we found a way to get the win.“
Going 12 points down was always going to be hard to come back from against quality opposition, but we found a way, we dug in and got the result so we are buzzing.
"To have someone like George [Ford] outside me makes the job so easy – he gets in the pocket – puts us in the right positions, and the little things he does that no one sees like talking off the ball is brilliant and his kicking game is fantastic as well.
"It's a massive win. Hopefully we can go four from four in the autumn series."
"Swing Low Sweet Chariot" echoed around Twickenham as the final whistle was blown, with England’s victory keeping the home team on track for a clean sweep in the autumn series.
