Gasser, the Big Air Olympic champion, led after two runs with a best score of 82.36, 0.01 ahead of her Japanese rival.
But when Onitsuka produced a final run of 85.33, Gasser could not respond and had to settle for silver in her first slopestyle event of the season after missing the opener in China.
Third on the day went to Norway's Silje Norendal (67.81) but it is Onitsuka who has established an early healthy lead atop both the overall and discipline standings after her victory at Secret Garden before Christmas.
Kleveland and Iwabuchi enjoy slopestyle success in Silvaplana
It was not a double Japanese victory to celebrate in Austria however as Takeru Otsuka – also the leader after winning in Secret Garden – slipped to fourth in the men's final on the third run.
The Japanese star had qualified first for the final but had no response as overall winner Norway's Mons Roisland produced a stunning final 88.75.
Chris Corning of the USA and Japan's Hiroaki Kunitake also passed Otsuka with their third and final runs to take silver and bronze respectively but Otsuka remains top of both the discipline and overall World Cup standings.
Kim and Totsuka take halfpipe glory in Aspen as White makes comeback
Kim and Totsuka take halfpipe glory in Aspen as Shaun White makes competitive comeback