The 25-year-old Australian claimed victory by the finest of margins with a turns score of 48.4 to Kingsbury's 47.7, which was used as the tie-breaker after both scored a total of 83.71.
The win offered some cheer for Australia after Jakara Anthony failed to retain her women's title on Wednesday.
"It hasn't sunk in yet. I'm speechless, super emotional, very proud," Woods told reporters.
"I didn't have any expectations this morning. I just wanted to go out and ski my runs and stay true to what I know I can achieve.
"It’s not often that you get one over Mikael, so I’ll take it when I can. He is an absolutely wonderful man... I always get advice from him."
Woods became the seventh Australian to win a gold medal at the Winter Olympics and the second to claim the men's moguls title after Dale Begg-Smith in Turin 2006.
He comes from a strong winter sports background as his mother Katrina competed in aerials skiing and his uncle Peter "Toppa" Topalovic is a renowned moguls coach in New South Wales.
Kingsbury, widely regarded as one of the greatest moguls skiers of all time, added a fourth Olympic medal to his collection, repeating his silver from Beijing 2022.
The 33-year-old Canadian also won gold at PyeongChang 2018 after picking up silver at Sochi 2014. He now holds the record for most Olympic medals in men's freestyle skiing.
Kingsbury recently extended his all-time World Cup wins record to 100.
Japan's World Cup leader Ikuma Horishima, who led earlier in the final with 83.44, claimed bronze after setting the benchmark with a rhythmic run packed with difficult tricks.
Sweden's 2022 Olympic champion Walter Wallberg finished fourth, making a strong comeback after an injury kept him out for most of last season. He only returned to action in December.