Woods, who had never previously finished on the podium at an Olympic or world championships, matched Kingsbury's score of 83.71 points in the men's moguls final.
The 25-year-old Australian secured the title with a turn score of 48.4, beating Kingsbury's 47.7. The Canadian had to settle for silver.
"I still can't believe it. I'm at a loss for words, so emotional, so proud," said Woods, who finished sixth at Beijing 2022.
"I didn't have any expectations this morning. I just wanted to ski and stay confident in my abilities. It's rare to beat Mikael."
Australian skier Cooper Woods in action during his competition at the 2026 Milan-Cortina Winter Olympics. (Xinhua/Hu Chao)
Kingsbury, the 2018 PyeongChang Olympic champion and two-time Olympic silver medalist, was competing in his fourth Olympics and had been leading with an impressive performance before Woods entered the fray.
"I feel great. I'm very satisfied with my skiing," said the 33-year-old athlete.
"It was a close match, right down to the tiebreaker, and unfortunately, I was unlucky in that tiebreaker. But I've worked really hard for this medal. I'm getting older, and at some point it felt like it would be impossible to get back to this level."
Japan's Ikuma Horishima, the defending world champion, won the bronze medal with 83.44 points after his final jump.
"I'm still chasing an Olympic gold medal, and it's an ongoing and difficult journey," Horishima said. "I've tried three times and now I'm on my fourth. It's a long road."
Defending Olympic champion Walter Wallberg of Sweden finished fourth, failing to return to the podium.
