The 32-year-old finished 1min 31sec ahead of Britain's Anna Henderson with world champion Chloe Dygert snatching third after a nasty fall, less than a second off silver.
"It means so much. Being away from Australia a lot of the year, being away from my family, that's given me the impetus to work really hard and make it all worth it," said Brown.
US rider Dygert is also racing the road race and track events and took her final corners with particular care, rather than racing out of them.
Competing in her final season, Brown came fourth in the same event at the Tokyo Games.
A day after a prolonged downpour drenched the opening ceremony, lighter rain persisted, adding an edge of danger to the race through the streets of the French capital.
Czech rider Julia Kopecky finished down the rankings and admitted the course was frightening.
"I fell and it hurt I can tell you," the 19-year-old told AFP at the finish line.
"The crowd motivated me to finish fast," she said, adding the road race next Saturday was her target.
Ellen van Dijk of the Netherlands was expected to medal but came 11th, having broken an ankle while training in Spain last month after returning to competition after having a baby in October.
Lotte Kopecky of Belgium also hit the deck hard in treacherous conditions.
"Because it was wet, we had to go a bit slower through the corners and that helped me take some little breaks along the way. I didn't really know that a lot of my competitors were crashing," Brown said.
"So it sounds like I was lucky to stay upright in the end. Sometimes that is just bad luck, or luck to me this time. So I'm glad that was the case for me. And I'm sorry for my competitors."
Brown revealed fans had warned her about the danger of a certain point of the course.
"At one corner the spectators were telling me to really slow down. So I had a feeling that maybe some people had, but I didn't know that there were so many."
Brown is enjoying a fine year, winning the national time-trial championships and the Liege-Bastogne-Liege one-day classic, but said this was the highlight of her career.
"Just to make Australia proud, winning the first gold medal for our nation," she said.
"Setting the medal table on its way. I hope I inspire the other athletes to push their limits and go after similar results."
Brown was fourth at the Tokyo Games with all three of the women ahead of her -- Annemiek van Vleuten, Marlen Reusser and Anna van der Breggen -- absent from the start line in the French capital.
