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 Russian starlets 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, becoming alpine skiing's oldest female medallist after a series of injuries which threatened to wreck her career and ruled her out of Sochi 2014.
"You've got to put things into perspective. Of ourse, I would have loved a gold medal but, honestly, this is amazing and I'm so proud."
- Ski cross chaos -
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Bjoergen reached 14 Olympic medals when she took bronze in cross-country skiing's women's team sprint free, outstripping compatriot Ole Einar Bjoerndalen, who has 13 in biathlon.
Bjoergen, 37, is also the second most successful woman at either the Summer or Winter Games, trailing only Soviet gymnast Larisa Latynina with 18 medals.
"I think I'll need to have time to myself and look behind me and look how I've been able to do this. It's still hard to understand it when I'm standing here."
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, 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.
Ridzik went down early in the race but he got up, clambered to the top of a slope and restarted his run, coming in behind the front two as Canada's Kevin Drury failed to finish.
France's Terence Tchiknavorian broke his leg and Canadian racer Chris Del Bosco was also taken to hospital after a sickening wipe-out.