In a wild event that rivals short-track speed skating for its unpredictable nature, Samkova had the fastest qualifying time, then avoided trouble by leading all the way in both her quarterfinal and semifinal heats.
She jumped ahead early in the final and stayed there, defeating silver medalist Dominique Maltais of Canada and third-place finisher Chloe Trespeuch of France.
American Faye Gulini wound up fourth and Lindsey Jacobellis of the United States, one of the medal favorites, failed to make it out of the semifinals.
The snowboard cross sends the competitors down a hill filled with bumps, jumps and hazards with only the top three in each heat advancing to the next round.
Jacobellis appeared to have won the race at the 2006 Olympics in Turin, but as she went over her final jump she reached down and grabbed her board in a showboating move.
That caused her to land poorly and she lost her lead to gold medalist Tanja Frieden of Switzerland. Jacobellis finished second in that race.
Four years ago she missed a gate in the semifinals and on Sunday she fell in her semifinal heat. Jacobellis won the "B" final, which was of little consolation since she finished seventh overall.
Samkova was able to get away with some showmanship of her own Sunday when she did a small fist pump while in the air on her last jump. She wears a drawn-on mustache when she skis and she showed it off as part of her post-race celebration.
Crashes are commonplace in this competition and defending gold medalist Maelle Ricker of Canada was involved in one during the quarterfinal heats. Helene Olafsen of Norway, bronze medalist at the most recent world championships, also crashed.
Americans had won three of the four previous snowboarding events contested at the 2014 Olympics.