Gasser, who finished 15th in the slopestyle event last week, put down a 96.00 with the final run of the day to snatch gold away from American Jamie Anderson.
The Austrian's combined score of 185.00 from her two best runs relegated slopestyle champion Anderson into silver with a 177.25 total, while New Zealand's Zoi Sadowski-Synnott took the bronze with a combined 157.50.
Gasser said deciding to go with something different for her third run had been key.
"I was standing up there and I knew I had the silver and I only could win and I was like, 'No, I'm going to go full risk and if it works out then I deserve this medal,'" she said.
"Thankfully it worked out."
The gold will go some way to making up for the Austrian's disappointment in the slopestyle, where high winds prevented any of the riders from laying down two clean runs.
Gasser said the slopestyle should have been postponed and that Anderson was the only one who wanted it to go ahead.
The big air event is making its Olympic debut in Pyeongchang and sees snowboarders hurtle down a ramp standing at 49 metres with a maximum slope angle of 40 degrees and perform spins and tricks to impress the judges.
The women's final was brought forward to Thursday as high winds are forecast for Friday, with the men's final scheduled for Saturday.
Anderson, who became the first woman to win two snowboarding medals at a single Olympics, said she was happier to win the big air silver medal than she was defending the slopestyle title she had won in Sochi four years ago.
"It feels better because we have great conditions and everyone was able to ride their best, so it feels rewarding," she said.
Sadowski-Synnott was another who took a risk with her final jump and while she could not pull it off perfectly, she was satisfied that she had given it a go.
"I've never done that trick before, but it's the Olympics, so I wanted to do something crazy," said the 16-year-old, who won New Zealand's second ever Winter Olympics medal.
Barely two hours later, another 16-year-old New Zealander, Nico Porteous, won his country's third when he took bronze in the ski halfpipe.
(Reporting by Peter Rutherford; Editing by Greg Stutchbury/John O'Brien)
