The Baby Blacks - who won the tournament from 2008 to 2011 - ended England's two year hold on the trophy.
England went in front through Max Clark, who burst through, before New Zealand hit back through Vince Tavae-Aso to lead at half-time.
Akira Ioane went over from close range to extend their advantage, as Otere Black added four penalties.
England beat South Africa in the semi-finals, while New Zealand went through to the showpiece after thrashing France in the last-four.
The New Zealand juniors performed the haka before kick-off, but England started confidently, going ahead through Bath centre Clark.
After a slow start, New Zealand got back into the game as Tavae-Aso powered over for a narrow 11-10 half-time lead.
Ioane bundled himself over early in the second half, before being sent to the sin bin, and although Rory Jennings kicked four penalties for England, they relinquished their hold on the trophy.
New Zealand won the World Rugby U20 Championship for the fifth time after beating England 21-16 in Italy.