Evi Sachenbacher of Germany claimed the silver while Norway's Anita Moen won the bronze.
The 25-year-old Russian was second quickest in qualifying and was second in her quarter-final heat.
But then Tchepalova stepped up a gear to win her semifinal and the final, quite comfortably.
The sprint gold was her second medal of the Games, having picked up a bronze in the 15km freestyle.
It also was her second gold medal in two Olympics - she won the 30K freestyle at Nagano in 1998.
"It was a very difficult victory for me," she said.
"Today was just my lucky day."
Sachenbacher was in a close battle with Moen, but managed to edge the Norwegian into third.
Czech World Cup leader Katerina Neumannova, who won the pre-Olympic warm-up sprint at Soldier Hollow in January 2001, set the fastest time in qualifying but went out after finishing last in her quarter-final.
The 58-woman field was narrowed during early morning qualifying.
The fastest 16 skiers moved into four elimination heats.
The top two skiers from each heat advanced to the semifinals.
The top two skiers in each semifinal then advanced to the final.