The bronze went to Michela Moioli of Italy.
After fighting through the qualifying rounds on the 1.1 km course, Baff sat in second place through much of the final race before surging into the lead by the midway point.
The 23-year-old claimed her first Olympic medal on a sunny day in front of Australian fans who cheered and waved inflated kangaroos on the side of the mountain in Livigno.
She jumped up and down on the podium and waved to the crowd.
Adamczykova added to her medal collection. She won the gold at Sochi 2014 and bronze at Pyeongchang 2018.
Moioli, who took gold in Pyeongchang, kissed her medal and wiped away tears.
Snowboard cross features high-speed races between four riders down a winding course filled with bumps and jumps.
The sport is known for being unpredictable, with competitors often knocking into each other and crashing. Winners are determined by fractions of a second.
Defending silver medallist, Chloe Trespeuch of France, was knocked out in the quarter-finals. The 31-year-old was competing in her fourth Olympics.