Compatriot Thor Hushovd, of Garmin-Cervelo, finished third to retain the race leader’s Yellow Jersey after 226.5km of racing from Dinan on the north coast to Lisieux in Normandy.
After the longest stage of the race, held in rainy conditions, Boasson Hagen proved the strongest from a bunch sprint that saw Australian Matt Goss of HTC-Highroad finish second.
Boasson Hagen only just squeezed into Team Sky’s squad after he picked up a dose of shingles in the week leading to the July 2 to 24 race.
And despite being a key helper in Bradley Wiggins’ bid for the Yellow Jersey, he repaid their faith by bringing the British outfit an historic first win in the world’s premier cycling event.
“It’s really nice to win this stage. It was a goal when I started this Tour so it’s great to finally achieve it,” said Boasson Hagen, who hails from a small village north of Lillehammer.
“It really great to stand up on top of the podium and look at all the people. With Thor having the Yellow Jersey, it’s a great day for Norway.”
Hushovd, who took the Yellow Jersey when Garmin won the team time-trial last Sunday, retained his overall lead of 01sec on Australia’s two-time runner-up Cadel Evans of BMC.
Despite being beaten by a bike length, Hushovd was quick to applaud the feat of his compatriot.
“It’s not too bad eh? A little country like Norway and we’ve got the stage win and the Yellow Jersey,” said Hushovd.
“Edvald has great potential. He’s won the longest stage of the Tour, and one which was very difficult. He’s got a great future ahead of him.
“He does well on most terrains, sprints, time-trials and he can climb well also.”
Belgium’s Philippe Gilbert, who won the opening stage and the Yellow Jersey for a day, could only finish seventh despite the hilly finale suiting his abilities.
However, the Omega-Pharma ace was consoled when he kept the points competition’s Green Jersey by a point from Spaniard Jose Joaquin Rojas of Movistar.
Gilbert said his bid for victory was hampered because he hesitated when he saw Australian rival Cadel Evans on his wheel, but he admitted that no one would have matched Boasson Hagen’s pace.
“Even a very good Goss and a strong Hushovd wouldn’t have beat him. He deserved the win,” said Gilbert.
Welshman Geraint Thomas reinforced his grip on the White Jersey for the race’s best-placed rider aged 25 and under. He sits seventh overall, 12sec behind Hushovd and just one place ahead of team-mate Boasson Hagen.
Spain’s defending champion Alberto Contador, who rides for Saxo Bank, finished with the front group in 48th place and remains 1:42 off the pace, 1:41 behind Evans and 1:30 behind rival Andy Schleck.
Friday’s stage is a 218km ride over mainly flat terrain from Le Mans to Chateauroux.