Tim Mikkelson scored two of the Kiwis' five tries as they followed up their women's team's 29-12 success against Canada at a rain-drenched Luzhniki Stadium.
Having disposed of reigning champions Wales in the quarter-finals and beaten Fiji 17-0 in the last four, the All Blacks would have been confident.
England, meanwhile, held off a second-half comeback to beat Australia 21-17 and then saw off Kenya 12-5.
Mikkelson put New Zealand ahead two minutes in, strolling in on the end of a three-on-one overlap, and scored again just before half-time and a minute after the second try from Tomasi Cama.
After a kick-dominated opening to the second half, Sherwin Stowers was brought down just yard from the line after a barnstorming run and Cama's pass skidded straight out of play to deny New Zealand a fourth try.
A Marcus Watson burst, England's most promising attack, ended when he slipped on the sodden surface and instead it was the Kiwis who scored again as Gillies Kaka jogged in down a deserted right flank and converted to make it 28-0.
And Waisake Naholo crossed after time expired to round off a one-sided win.
In the women's final, Portia Woodman starred with two tries, including a solo run from halfway to take her total for the tournament to 12.
She was also involved in Kayla McAlister's score straight afterwards as New Zealand took a decisive three-score lead late in the game and celebrated victory by dunking coach Sean Horan in the worst of the mud on the halfway line.