Joe Launchbury crossed for England's only try and flyhalf Owen Farrell kicked six from six, giving the hosts' belief they could pull off a second straight win over the world's top-ranked side and clinch a third successive November victory over Rugby Championship opponents.
The All Blacks wrestled back the initiative, though, as Savea's 64th-minute try and Aaron Cruden's late penalty saw them home.
"Credit to New Zealand they are a champion side and they showed it in the end," England coach Stuart Lancaster said. "If you went into the England dressing room, we are desperately disappointed to have lost to a team that has been unbeaten all season."
The All Blacks' only defeat since August 2011 stretching back 34 games remains the reverse to England last year and their brilliant run of results has sparked a debate over whether they are the best team in world sports.
Lancaster thinks so he said so this week but they were given a going-over by England's forwards in the middle 40 minutes of the match, sending the All Blacks back in the collision and scrum and leaving New Zealand coach Steve Hansen shaking his head in the stands.
"We mauled New Zealand to death," England backs coach Andy Farrell said.
Maybe it was just a coincidence, but the departure of Carter the world's premier pivot of the past decade heralded the start of England's renaissance.
He became the fifth All Black to 100 caps, marking the occasion by wearing golden boots with "DC100" on them, and had kicked eight points by the time he hobbled off with an injury that's "been rumbling away for a while," according to Hansen.
"He would have loved to have been out there for 80 minutes," McCaw said, "but he's got that milestone and got a bit of a smile on his face."
It is a testament to the character of this young, bold England team missing six British Lions that they didn't wilt after Read's 15th international try, which was converted to make it 17-3 and made him the most prolific No. 8 in rugby history eclipsing the try record of compatriot Zinzan Brooke. It was also the fifth straight game in which he has scored.
Read had also set up Savea's try inside two minutes, offloading deftly as he was being ushered into touch by three tacklers to allow the winger, who also scored two tries here last year, to romp clear untouched.
Fourteen points down against the best team in the world, England made a statement of intent by turning down three kicks at goal to go for attacking lineouts. After the third lineout, Billy Vunipola was dragged over the line in a maul but the video referee couldn't see the ball grounded and ruled no try.
From the resulting scrum, the ball was kicked forward by England's pack but Read fumbled and Launchbury pounced to ground on the dive from close range.
Carter went off, Cruden kicked a penalty but England was given cause for hope when Read was sin-binned in the 33rd after persistent team infringements.
Farrell kicked three straight penalties, two while Read was off, and it needed something special for New Zealand to regain its foothold.
Nonu provided it.
After Charles Piutau was denied a try by a last-ditch tackle from Mike Brown, the All Blacks recycled to the left and Nonu offloaded brilliantly despite being tackled by England strongmen Ben Morgan and Courtney Lawes, and Savea ran through three opponents to ground.
Cruden's penalty in the 71st, giving him eight points for the match, ended England's comeback hopes.
