China's Eileen Gu, who had been hoping to convert her Beijing 2022 silver medal in the event into gold this time, came in second after tumbling at the start of her last run.
Canada's Megan Oldham, 24, made it to the bottom step of the podium despite a big crash on her second run.
Giving herself a day-late birthday present, Gremaud skied well above the already very high bar set by Gu, with three spectacular runs, wearing the Swiss flag like a cape on her last run having already ensured herself the gold medal.
On a crisp and sunny day, Gremaud kicked off the final performing - for the first time ever by a woman - an elite level trick known as the nose butter double cork 1260.
In this trick the skier presses the tips of the skis on the takeoff to start the spin and then performs a double cork 1260, two distinct off-axis, inverted flips combined with three and a half full, horizontal rotations.
Known for her variety of tricks on the slope, the Swiss champion veered towards very technical ones followed by breathtaking acrobatic jumps in her second run, which earned her the top score of 86.96, just pipping Gu's first-run score of 86.58.
Despite the big crash on her second run, Oldham picked up in the third run, soaring through the rails and performing conservative yet still very acrobatic jumps at the end, winning her a score of 76.46.