Zagitova was breathtaking in the Russian-dominated short programme, breaking the world record set just minutes earlier by her team-mate, 18-year-old Evgenia Medvedeva.
It put the Russians top of the standings ahead of Friday's free skate, where Zagitova will attempt to become the youngest women's singles figure skating champion since Tara Lipinski in 1998.
They also look set to win the first gold of the Games for the Olympic Athletes from Russia, who are competing as neutrals after Russia's national team was banned over a major doping scandal.
"But on the ice, we must fight, I feel like it's a little war, when you skate you are alone," added the double world champion.
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America's Vonn, 33, was aiming for a second downhill title in her final Olympics, but it was not to be as she finished third behind Italy's Sofia Goggia and Ragnhild Mowinckel of Norway.
But the 2010 winner was delighted to reach the podium -- the oldest female alpine skier to do so -- after a series of injuries threatened to wreck her career and ruled her out of Sochi 2014.
"You've got to put things into perspective. Of course, I would have loved a gold medal but, honestly, this is amazing and I'm so proud."
- Ski cross chaos -
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There was disappointment for the United States when their men's ice hockey team, missing NHL players after a row over money, crashed out 3-2 in the quarter-finals against the Czech Republic.
In other action today, Russian skier Sergey Ridzik recovered from a crash in the ski cross final to take bronze, behind Canada's Bredy Leman and Marc Bischofberger of Switzerland.
The competition, where four skiers race each other down a twisting track featuring a number of jumps, was marred by a series of heavy falls.
France's Terence Tchiknavorian broke his leg and Canadian racer Chris Del Bosco was also taken to hospital after a sickening wipe-out.
Later today, the women's bobsleigh will feature trailblazing Nigeria, who are the first athletes from their country to compete at a Winter Olympics.