Unaffected by a big crash in the middle of the peloton within sight of the finish, Boasson Hagen easily won a fast and furious downhill bunch sprint ahead of Germany's Gerald Ciolek and Slovenian Borut Bozic.
Sky's 26 wins make them the second most successful team of the season behind top Belgian Classics squad Omega-Pharma Quick Step, who have 30.
"It's a nice day for the team, we have the yellow jersey and we did a good job to keep Bradley up there," said Boasson Hagen, a former Tour de France stage winner and victorious in his home race, the Tour of Norway, last month.
"It wasn't easy, but I got a good gap, and I'm happy. We're riding really strongly right now, with the lead for Bradley and now a stage win for me."
Belgian Classics top rider Philippe Gilbert attempted to ambush the pack as it roared into La Clayette but his bold move fizzled out 500 metres from the finish.
Defending champion Wiggins remains in the overall lead ahead of the race's first big challenge on Thursday, a 53.5 kilometre individual time trial. Australian Cadel Evans is in second, a second back, and Ukrainian Andriy Grivko in third.
"We'll keep our fingers crossed for Bradley," said Boasson Hagen, "but it's going well so far."
The race finishes on Sunday in Chatel.