Defending champion Lebedeva's first jump of 14.95 metres, the furthest in the world this year, put her out of reach of the rest of the field and made up for her disappointment at last year's outdoor championships.
Lebedeva, who is also Olympic long jump champion, was hot favourite to win the outdoor triple jump title in Helsinki but was forced to bow out with an Achilles injury.
"I am very glad I won Russia's first gold. We won a couple of medals yesterday and today with mine and Anna's, it's even better," said Lebedeva, who is also the world indoor record holder.
Their triumph was followed shortly afterwards when Russians Yaroslav Rybakov and Andrey Tereshin took one-two in the men's high jump.
"I am sure we can do very well here and beat the Americans and everybody else," Lebedeva told reporters.
She received a congratulatory hug and kiss from her friend Yelena Isinbayeva, who was gunning for another Russian gold in the pole vault.
Pyatykh, who took bronze at last year's worlds, was out of the medals until her final attempt when she leapt 14.93 metres, further than she had ever jumped before, to roars of approval from the stands.
"I am known as 'the sixth round woman' and I proved that today," she told Reuters.
Yamile Aldama, of Cuban origin but competing for Sudan from 2004, had to be content with bronze after her best jump of 14.86 metres.
Jamaican Trecia Smith, who took first place in Helsinki in Lebedeva's absence, and had been tipped for a medal on Saturday, was pushed into fourth place by Pyatykh's final leap.
