Veteran Marianne Vos of the Netherlands took silver ahead of Belgium's pre-race favourite Lotte Kopecky in a photo finish.
Hungarian rider Blanka Vas just missed out on the podium.
"I feel like it's a dream come true," said Faulkner. "It's the best feeling in the world and I don't know how to describe it."
Vas and Vos had led over the entire closing circuit of the French capital until Kopecky and Faulkner caught them with the finish line 2km away.
As the four passed the Louvre museum Faulkner launched an attack to break free of the lead group, and surged to the finish, the other three riders left lagging well behind.
Faulkner, a former rower from Alaska who will also compete in track cycling next week, said her tactics were born of necessity.
"Kopecky wanted to catch the front two, so I knew she'd ride with me. I also knew that if we caught them, then I had to attack because I couldn't beat any of them at the line," said Faulkner.
The 31-year-old grabbed an American flag and lapped up the support of the crowd after crossing the line, admitting it took time for her victory to sink in.
"I had to double and triple check that I won gold. I knew it but I didn't know it," said Faulkner.
'Racing to win'
Faulkner did not initially qualify for the road race but took the place of Taylor Knibb, who opted to focus instead on the time trial and triathlon.
A cross-discipline rider herself, Faulkner also has major hopes in the team pursuit.
"I'm racing team pursuit in two days and so I said I'd only do the road race if I felt strong and felt I had a chance of a medal. So if I was racing, I was racing to win," said Faulkner.
Behind her the other three slugged it out for the two remaining medals, with Vas the odd one out.
Kopecky, who finished fourth in Tokyo, was desperate to avoid a repeat disappointment.
"After Faulkner got away we looked at each other. She is a stronger sprinter than me. I just wanted a medal, so I'm very happy with my bronze," said Kopecky.
Around 500,000 people lined the streets of Paris for the men's road race on Saturday, with vast crowds again turning out for the women's event.
Both races saw cyclists speed through some of the most picturesque streets of the capital, including the famous Montmartre hill, while the start and finish line was in front of the Eiffel Tower.
Ninety-three riders from 58 nations set off in bright sunshine on Sunday with Burkina Faso's Awa Bamogo the first to attack as the peloton departed Paris for the countryside.
A second sustained attack included the Hashimi sisters from Afghanistan, but the group was swallowed up as soon as the real action got going on the first of three climbs to Montmartre.
