Evenepoel suffered a mechanical less than four kilometres from the finish, on the Carousel du Louvre, raising his arm for assistance before clapping and waving at his team to deliver a new bike in a scene of sheer panic.
The change was made swiftly, however, and he powered to the line after he had made the decisive move 15km from the finish, in the run-in to the second of three punishing ascents of the Butte Montmartre.
His brutal attack left Valentin Madouas, who was hovering 1:15 behind when Evenepoel's incident occurred, gasping for air but the Frenchman hung on to take silver after the 273km road race.
Madouas' teammate Christophe Laporte won the sprint for third from a small group.
Evenepoel raised his arm again in the final kilometre but this time it was a pre-celebration before stepping off his bike as he crossed the line for a photo with the Eiffel Tower in the background.
"What a place to win this. Honestly I feel sick. So proud to win this and to be the first ever to double it, history, no ?," a beaming Evenepoel, who finished third overall in the Tour de France last month, told reporters.
"You are never sure enough. I felt that his legs were getting empty and I knew the kicker where I dropped him was a kicker that really suited me. It was just pushing, pushing, pushing to the line.
"I really feel sick from the effort especially with the stressy moment with 4km to go, I got a straight puncture. I had to change bike, bit of stress but I had time enough."
Dutchman Mathieu van der Poel, one of the pre-race favourites, made a move on the steepest part of the Rue Lepic but could not open a decisive gap and ended up a disappointing 12th.
It was another memorable day for France, who have been delighting the home crowd with top-notch performances at the Games and although they were not among the favourites, Madouas and Laporte delivered.
"(Coach) Thomas (Voeckler) said to me yesterday: 'Get a head start, it'll take you a long way'. I put in an attack and we went out. I was waiting for the champions to come back and I had to stay on Remco's wheel as long as possible," Madouas told reporters.
"He was a cut above the rest, even though I could see him in the distance in the finale. To come second here in Paris, in a setting like this, I have nothing to say."
