The versatile Norwegian, riding for the African-based Dimension Data team, was part of a nine-man lead group speeding towards a roundabout 2.5km from the finish line of the 222km trek from Embrun on stage 19.
While seven of them veered left, the long way round, Boasson Hagen and Sunweb's German rider Nikias Arndt swerved to the right -- instantly catapulting themselves clear of their pursuers.
Boasson Hagen, a class act who won two stages for Team Sky in 2011 but who had suffered torment this year with two runners-up finishes and two third places, then outclassed Arndt to take the victory by a comfortable five seconds.
"This morning we watched a video of the finale and we were instructed to be on the right side," the 30-year-old, who lost a photo-finish to Marcel Kittel on stage seven, said.
"It was shorter. Everyone else went on the left, except Nikias Arndt. It was the right moment to go.
"I had studied the course and I knew I had to go right in that last roundabout. Afterwards, I managed to go solo and I was so happy when I crossed the line. I've been so close so many times. It's really nice to finally get this victory for the team and for myself as well."
It was a joyous moment too for team boss Douglas Ryder, whose outfit uses it's Tour income to provide bicycles for Africans in rural areas.
With the team's sprint king Mark Cavendish crashing out early in the Tour, it looked as though Dimension Data would not have the stage win that does so much for the Qhubeka charity which it promotes and supports.
Ryder could hardly contain himself at the finish in Salon-de-Provence and was full of praise for Boasson Hagen.
"An amazing way to win it," he said. "We plan for every metre of the end of these stages and we knew he had to go around the roundabout to the right. We gained 10 metres. But Edvald still had to have the power to finish it off."
Cavendish, who was watching at home with a fractured shoulder, joined in the celebrations for his team mate who is so often the unsung hero in the Manxman's sprint victories.
"Yesssssssssss!!!!!! Edvald!!!!!! Finally!!" he said on Twitter. "I'm in tears. You absolute hero!"
(Reporting by Martyn Herman, editing by Pritha Sarkar)
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