Scrum-half Aaron Smith scored two tries as the All Blacks produced a first half that coach Steve Hansen called "as good as you can get".
Fly-half Aaron Cruden kicked nine points and his replacement Beauden Barrett added a late conversion as the hosts won the three-Test series 3-0. England fly-half Freddie Burns slotted two first-half penalties and converted Marland Yarde's second-half try.
The victory meant Hansen's side equalled the record amongst Tier One Nations jointly held by the 1965-69 All Blacks and the 1997-98 South African teams. They can beat the record against Australia in Sydney on August 16 in their opening Rugby Championship match.
The All Blacks stamped their authority in the first 20 minutes as their forwards sucked in England's players to narrow the defence then cut their backs to shreds out wide. Burns slotted his second penalty to cut the deficit to 15-6 before Billy Vunipola committed a high tackle on Cruden and given a yellow card. Smith then ran the perfect support lines to cross twice as the All Blacks again cut through the England defence and established a 29-6 half-time lead.
Winger Yarde crossed just after the break, but apart from that England could not breach a smothering All Blacks defence. Savea completed his hat-trick two minutes after the final hooter had sounded as the hosts kept the ball alive, Barrett adding the conversion.
England head coach Stuart Lancaster admitted he read his team the riot act after the first half: "We had some sharp words at half time and we showed a lot more urgency and intensity in the second half and," he said. "The objective was to win the series and we haven't achieved that. But we've shown enough to demonstrate we are a young team on the up."
Australia also wrapped up a series whitewash with a 39-13 victory in the third Test against France at the Allianz Stadium in Sydney. Israel Folau scored two of Australia's five tries, with debutant Will Skelton, Michael Hooper and Nick Phipps also crossing.
Fly-half Bernard Foley added four conversions and two penalties as the Wallabies made it seven Tests in a row. France could only muster a converted try from Guilhem Guirado in the second half plus two penalties.
Meanwhile, a second penalty try for South Africa two minutes from time gave them a 31-30 victory over a desperately unlucky Wales in Nelspruit yesterday.
The tourists were tantalisingly close to a first victory on South African soil having proved the more physical and clinical side against a rattled home team.
Wales, who at one stage played with 13 men, scored three tries through centre Jamie Roberts, wing Alex Cuthbert and hooker Ken Owens. Fly-half Dan Biggar converted those and added three penalties.
South Africa's points came through the two penalty tries and further scores from wing Cornall Hendricks and Willie le Roux. Fly-half Morne Steyn booted four conversions and a penalty.