France, who led for the first two legs of the race before stumbling, took silver while Germany grabbed bronze amid light snow at Whistler Olympic Park.
Russia took command of the race in the third leg when Olga Medvedtseva turned a slight deficit into a 45-second advantage heading into the final round.
Medvedtseva, who did not miss a target, denied her performance was the difference.
"We did good for the entire duration of the course," she said. "I was getting clear information about how all my competitors were doing.
"I was very aware of my lead and concentrating only on one thing, shooting. Because a relay depends on clean shots."
Olga Zaitseva cruised home for the Russians, entering the final loop by herself to a wildly cheering and flag-waving crowd.
She pumped her right arm skywards 60 metres before the finish line, then looked back to see how big a lead she had over second-placed France.
Zaitseva then blew kisses to the adoring crowd before crossing the finish line with a delicate curtsy and both arms raised in celebration before being swamped by her team-mates.
The Russians completed the course in 1:09:36.3, nearly 33 seconds before France, who fell out of gold medal contention when third leg Marie Dorin was forced to run two penalty laps.
"I didn't feel well," said Dorin, a bronze medal winner in last week's 7.5km sprint. "I tried to catch up. I have to thank my team-mates."
Germany was second after the third leg but lost ground en route to the finish. Anchor Andrea Henkel did not run any penalty laps but could not keep up on the skis.
Neuner, winner of three medals in Vancouver, said she was exhausted and decided not to participate in the relay.
Her compatriot Martina Beck admitted she cried when Neuner told her she would not compete in the relay.
"At first, I couldn't say anything," said Beck, who skied her team's third leg. "I was so shocked. I had lots of pressure on me today. It was probably the hardest race of my life."