This is actually the Plot of Ghost Recon for the Xbox and PS2 (Released in 2001)

According to the Game, In August 2008 Russian troops invade Georgia through South Ossetia. After Georgia falls, the Caucasus region is vulnerable to further attack. The Georgian government, UK, Germany, and the U.S. all protest the Russian invasion, but Moscow ignores them. Russia then focuses on invading the Baltic States on Lithuania, Latvia, and Estonia. The Russians launch their attack early and overrun the Baltic States within days. After cutting off the Russian reinforcements, American forces fight to push the Russian Army out of the Baltics. Victories are won within the next months in Utena and Rezekne, and finally, NATO reaches Vilnius, Lithuania. The city was almost leveled after the invasion, but it is eventually liberated,forcing the Russian Army to abandon the invasion.

After that the US invades Russia and "liberates" Moscow.