The outright favourite, who came into the event after winning three of the last four World Cups, won with a score of 26.77.
He edged out Finn Mikko Ronkainen (26.62) and American Toby Dawson (26.30).
Fellow Australian Nick Fisher achieved his best ever result in a top tier competition finishing 12th (23.39).
Begg-Smith seamlessly skied down the Sauze D'Oulx course to record Australia's third ever Winter Olympics gold medal, after Steven Bradbury (short track speed skating) and Alisa Camplin (freestyle aerials) both won in 2002.
"It's unbelievable, it's awesome, it's what I've always wanted," Begg-Smith told reporters after his win.
"I'm very happy to do it for Australia."
The 21-year-old, born and raised in Canada, was the last competitor down the course.
"I was happy to run last because you get to know how everyone else did and I knew there were some good scores up there so I was sure not to make any mistakes," Begg-Smith said.
"I knew that was the best run I could do at the time and that's what I wanted to do."
He scored well with his tricks -- an inverted jump with cross and an off axis 720 -- and had a reasonable run time but it was for his turns, which account for 50 percent of the total score, that he again did best.
Brought up in Vancouver, Begg-Smith came to Australia as a 15-year-old with his brother Jason, who finished 29th in the event.
They had decided they could no longer participate in the Canadian moguls skiing program because it clashed with their business.
The pair run an internet advertising company which has been the source of much speculation.
At the post-event press conference, Begg-Smith fielded as many questions about the nature of what the business was involved in as he did about actually winning a gold medal.
Michael Robertson, the other Australian in the event, finished 24th.