The women set the tone with a comprehensive 29-12 thumping of Canada in their final.
The All Blacks Sevens immediately took up the challenge to thrash England 33-nil in their final.
Both finals were played in soaking conditions as thunderstorms blitzed the Russian capital.
The men were earlier taken from the field during their semifinal win over Fiji for safety reasons with thunder and lightning circling the ground. Play was suspended for an hour.
Both the men and women returned to play super wet-weather rugby and claim the titles, sending powerful messages as the sport gets set to make its Olympics debut in 2016.
The victories complete a stunning global domination for New Zealand rugby at the highest levels.
New Zealand now owns the World Cups in 15s and sevens in both men’s and women’s divisions. They also hold the world series crowns for sevens in both the men’s and women’s games.
The men made a stunning start to their final with speedsters Sherwin Stowers and Tim Mikkelson combining to slice England apart.
A cleverly worked try to Tomasi Cama off a lineout win kept the momentum going New Zealand’s way and Mikkelson provided a crucial strike right on halftime. With Cama banging over the conversions, the Kiwis led 21-nil at the break.
They were content to employ a kicking game in the second half, looking to play in England territory.
The English, under pressure, were pressured into mistakes as New Zealand saw out victory to claim their first World Cup since 2001.
Bright young stars Gillies Kaka and Waisake Naholo rounded things off with a late try as New Zealand completed a record margin in a final.
“This is truly humbling. I’m lost for words. I’m just so proud for the boys,” said an emotional New Zealand captain DJ Forbes.
Master coach Sir Gordon Tietjens praised the work ethics of his squad to finally reclaim the cup.
“It’s been a long time between drinks,” he said.
Canada won the Plate, while the hosts Russia won the Bowl.-stuff.co.nz