The Russians led by several points through much of the game, although the French roared back in the middle of the second half to level at 14-14 before again trailing to a fierce attack.
When the final whistle was blown, Russia's players fell to the ground and embraced, while the disappointed French walked off, some wiping away tears.
"We did what we wanted... everything for me is like a dream," Russia's beaming Anna Sen, 25, told reporters, adding the team sang 'We came here to win' in the locker room.
France had strong support from the mostly packed arena, with shouts of 'Les Bleus!' from their fans, but although they won their first Olympic women's handball medal there were regrets.
"We had the way to beat them, but we failed at some of the shots," said France's Tamara Horacek. "The Russians play from all sides, they know how to do everything."
Earlier on Saturday, defending champions Norway found some solace for not making it into the final by overpowering the Netherlands to take bronze.
(Editing by Nina Chestney and Ken Ferris)
