Ripa trailed Ukraine's Julija Batenkova by more than 30 seconds haflway through the 15-kilometre race, but managed to inch closer and closer.
Sveriges Radio reported on Monday that she managed to beat the Ukrainian by 3.9 seconds as she crossed the finishing line in Russia.
Ripa, who lost her leg to cancer age 15, is a former international swimmer who took up cross-country skiing just a few years ago.
"Cross-country skiing opened up a whole new world," she writes on her blog. "To make your way in snow, which isn't usually much fun or very easy with a prosthesis, was a powerful feeling."
The 42-year-old was featured last week as The Local's Swede of the Week.