On a good day for his Etixx-Quick Step team, who earlier won the team time trial at the world championships in Doha, Gaviria jumped away from the pack 300 meters from the line and never looked back.
Arnaud Demare (FDJ) was second ahead of Jonas van Genechten (IAM Cycling) at the end of the 252.5 km race from Dreux.
“This is the most beautiful win of my career," Gaviria said. "I knew how important and big this race was, I know its history, and this motivated me to get the victory today.
"It was tough and fast today, but I was fresh in the finale, when I decided to take advantage of a corner which slowed down the peloton before the last straight.
"As soon as I attacked, I went full gas to the line and managed to hold the pack at bay. I am very happy and I want to thank the team for the support I got.
"It was my final race of the year in this kit and this makes the success very special. Also, to get news that the team won the team time trial world title gives me even more satisfaction."
The world championships elite men's road race will be held in Doha next Sunday.
“In Doha it’s going to be a completely different story and the race will be made even more difficult by the heat, but I’m going there confident, relaxed and in good condition, so we’ll see what will happen," Gaviria said.