England captain Sean O'Loughlin scored a late try in the wet Wigan stadium, after forward Elliot Whitehead scored twice to the visitors' own three tries.
O'Loughlin powered over eight minutes from time to put England 20-6 ahead against the world's top-ranked side, but the Kiwis fought back in the closing minutes, Samoan-born Roger Tuivasa-Sheck and Jordan Kahu grabbing tries to set up a tense finale.
However England hung on to seal their first series win over either World Cup winners Australia or No.1-ranked New Zealand since 2007.