The 34-year-old nailed a triple somersault on the opening jump of the final for a score of 98.01 and then watched as the other three finalists all failed to produce clean landings.
Tsuper made her Olympic debut for Ukraine at Nagano in 1998 and returned last August, after taking two years out of the sport to start a family, for one last shot at an Olympic title.
She squeaked into the final by snatching the 12th and last qualifying spot but topped the leaderboard in the first of the three knockout final rounds, scraped into the final round, then gatecrashed the expected China-Australia showdown.
Roared on by the Russian crowd, she hit the ramp at 60 kilometres per hour off a reduced run-up, spun and twisted through the mountain air before landing safely to set a standard none of her rivals were able to match.
"I'm very happy to be Olympic champion," said Tsuper. "I was showing my fight and my power, that I could do everything and I put trust in myself. Fortune was on my side today.
"I wanted this victory. My jumps and my tricks were very difficult and I could compete with the other participants. The crowd really helped me today."
China's Xu Mengtao, who has been the woman to beat in the sport over the last four years, had the tidiest landing of the three remaining finalists and claimed silver with a score of 83.50.
"Before the competition we all wanted to get a gold medal, but I didn't get the chance," said the 23-year-old, who injured her arm trying to stay upright on her final landing.
"I tried to land straight but I didn't succeed. There was something wrong with my judgement."
Australia's defending champion Lydia Lassila was attempting the most complicated manoeuvre in the final but her skis slipped out from underneath her on the landing slope and she took the bronze with 72.12.
Lassila, who had taken three years out of the sport to have a baby and only returned this season, was reduced to tears as she relinquished the title she won at the Vancouver Games four years ago.
"I was always going to go into the Olympics with the approach of all or nothing. I'm the first woman to do a full-double-full-full," she said.
"It would have been great to land that jump but I was stretching for my life and I just couldn't get there.
"I didn't have the easiest of days but I made it through each round. I am so proud of myself. I am very emotional."
Li Nina, who has also missed much of the last four years after a retirement and a serious knee injury, saw her dreams of adding a gold to the silvers she won at the last two Winter Games ended with a spectacular crash landing on the second jump of the final.
China's powerhouse team had three jumpers into the final 12 but again failed to land a first gold medal in a sport they have largely dominated at world championship and World Cup level for the last eight years.