Flyhalf Freddie Burns slotted two first half penalties and converted Marland Yarde's second half try for the visitors who impressed on their tour with their combativeness and willingness to play a wide game.
The victory ensured Steve 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 and have the opportunity to eclipse it against Australia in Sydney on Aug. 16.
After tight clashes in the first two matches of the series, the All Blacks stamped their authority on Waikato Stadium 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.
Savea crossed the tryline three times in that opening quarter but was only awarded two tries with the final pass on his potential third drifting forward after yet another clinical interplay between the pack and backline.
Burns slotted his second penalty to reduce the deficit to 15-6 before Billy Vunipola was harshly adjudged to have committed a high tackle on Cruden and given a yellow card by Jerome Garces.
Scrumhalf Smith then ran the perfect support lines to cross twice as the All Blacks again cut through the England defence with ease and establish an imposing 29-6 halftime lead.
England winger Yarde crossed shortly after the break as the visitors finally imposed themselves on the game and while they had several opportunities to score were unable to breach a desperate smothering All Blacks defence.
Savea then completed his hat-trick almost two minutes after the final hooter had sounded as the hosts kept the ball alive, with Barrett adding the conversion.
(Reporting by Greg Stutchbury in Wellington; Editing by Sudipto Ganguly)
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