Boasson Hagen, who was edged out in a photo finish by Marcel Kittel on the seventh stage, was part of a 20-man breakaway but made a winning solo bid inside the final 3km as Nikias Arndt came second and Jens Keukeleire third.
“I’m so happy, it worked out really well. I didn’t have to do the photo finish this time, so it’s really good,” said Boasson Hagen, 30.
It was his third Tour stage win following another two in 2011 when riding for Froome’s Sky team.
And it came about after he and Arndt stole a march on their breakaway rivals by going around the shorter side of a roundabout.
“I’d been looking through the video (of the stage) before and I knew the right side of this one was shorter,” said Boasson Hagen of the roundabout around 3km from the finish.
“Nikias made an attack and I followed him. Then when I did a final attack he wasn’t able to follow, so I’m really happy.”
Briton Froome kept hold of the race leader’s yellow jersey ahead of Saturday’s decisive time-trial in Marseille after a leisurely stroll in the saddle for the peloton.
Frenchman Romain Bardet remains second at 23sec with Rigoberto Uran of Colombia third at 29sec.
“Tomorrow’s a day where you have to leave everything on the road,” said Froome.
“Tomorrow, it’s still all to race for, there’s still 30 seconds between the top three in GC — the race is still very much on.”
The large group of escapees broke clear early on in the 222.5km stage — the longest of this year’s race — that started in the Alps before ending close to the Mediterranean.
Reigning champion Froome’s Sky team-mates at the front of the peloton showed no interest in chasing them down and so the gap gradually increased to over 10 minutes.
Inside the final 20km, an attack from Belgian Keukeleire, who was voted the most combative rider of the day, split the lead group with a front nine forming.
And the winning move came just inside the final 3km when the nine riders came to a roundabout.
– ‘Wrong way’ –
Seven went to the left, which proved to be the longer route, while Arndt and Boasson Hagen stuck to the shorter right side, emerging with a clear lead of around 10 bike lengths.
“We took the roundabout the wrong way and he (Boasson Hagen) took the shortest way,” admitted Keukeleire.
“We’d talked about it before, we knew there were a lot of roundabouts and we needed to go the right way.
“I didn’t think about it (at the time) but when we hit the roundabout it struck me we went wrong way — and he was away.”
Arndt pushed hard and then moved over to let Boasson Hagen take the lead, but the Norwegian simply rode the German off his wheel and powered on to the finish to win by five seconds, with Keukeleire leading home the other seven 17sec back.
“I don’t know if everyone did the reconnaissance before, but when everyone went left I knew I had to go right,” added Boasson Hagen.
“Sometimes you forget what happens in the (morning) meeting and follow the rest.
“Maybe they didn’t know it but I knew it and did the right thing and I’m happy for that.”
The trundling Sky-led peloton arrived 12 and a half minutes after their former team-mate.
Saturday’s 22.5km time-trial around Marseille offers Bardet and Uran one last chance to try to dethrone three-time winner Froome, who is widely considered the best time-trialist of the three.
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