In the Tour's first big shake-up, the Sky squad was dominant up the first summit finish to allow Christopher Froome to win the seventh stage from Tomblaine to La Planche des Belles Filles ski station.
The 199-kilometre trek into the Vosges range went a long way toward shaping the three-week race as experts predicted before the start — a showdown between Wiggins and defending champion Cadel Evans.
In a five-rider breakaway group on the final climb, Evans tried an attack just before the super-steep climb in the last kilometre — but Froome beat him by two seconds as Wiggins hugged close to the Australian's back wheel.
After the finish, compatriots Wiggins and Froome hugged, with Wiggins becoming the first Briton since David Millar in 2000 to wear the yellow jersey.
Cancellara, the Swiss time-trial specialist who had worn the jersey since winning the opening prologue a week ago, is 1 minute, 52 seconds behind Froome — but more importantly 1:50 back of Wiggins.
The Sky leader, who began the day seven seconds behind Cancellara in second place overall, leads Evans by 10 seconds. Vincenzo Nibali of Italy was fourth to climb to third overall, 16 seconds behind.
"It's a great day for the team, we won the stage and took the yellow jersey," said Wiggins. "This is my first time in the yellow jersey. It's incredible — it's been a dream of mine since I was a kid."
Giro d'Italia champion and Victoria native Ryder Hesjedal pulled out of the race before the start of the stage after being injured in a multi-rider crash Friday.
Wiggins has more breathing room than Cancellara had, with only five riders within a minute of his time — including Denis Menchov of Russia, who won the 2009 Giro and Spanish Vuelta in 2005 and 2007. The Swiss rider, by contrast, had had 22 riders within 48 seconds of his time before Saturday's ride.
Wiggins, a three-time Olympic track gold medallist , became the pre-race favourite after winning the Paris-Nice, Tour de Romandie and Criterium du Dauphine stage races earlier this year.
With two time trials and more climbing days in the Alps and Pyrenees still to come, Wiggins played down speculation that he might've taken the lead too early with the finish in Paris on July 22.
"You can't get too cocky in this race and choose when you take the yellow jersey. I'd much rather be in yellow than in hospital — like half the peloton," he said, referring to crashes on Friday that forced at least 12 riders to quit the race.
Wiggins crashed out of the 2011 Tour because of a broken collarbone and said he felt "lucky" he has been trouble-free this year.
Froome was part of the Team Sky phalanx that powered up the final climb. With most rivals falling away, the Kenyan-born Briton overcame Evans' late surge to burst ahead to the finish.
"He was really strong. He controlled the last two to three kilometres well," Evans said of Froome. "I thought I could anticipate it thanks to the turn and gain some speed to launch the sprint — but he had the legs and overtook me."
The 35-year-old Australian senses he's in for a challenge from Sky.
"With Wiggins on a team like that, it's going to be difficult," Evans said.
Froome, who took the polka-dot jersey as the Tour's best climber, said he was surprised Evans couldn't keep pace. The Australian was puffing and his face glistening with sweat as he crossed the finish.
"I kept waiting for him to go, but he never really went. To me that says one thing — that he didn't have the legs," Froome said. "It really wasn't a big acceleration that I put in. I went for it and just coasted toward the line.
"Hopefully he's not holding anything back, and he's not going to surprise us in the next few days," Froome said. "I think that he and Bradley looked to be quite on par."
Wiggins said he is focusing on Evans.
"You saw it today, Cadel never gives up," Wiggins said.
The stage marked the first of three summit finishes in this 99th Tour edition. Nimbler mountain specialists seized the limelight after a first week dominated by sprinters across the flatter regions of Belgium — where the race began June 30 — and northern France.
The final ascent, at 5.9 kilometres, was relatively short as far as the Tour's biggest climbs go. But it was steep, with a gruelling 14-per cent gradient in the last 500 metres.
Seven riders broke away from the pack after 15 kilometres and held the lead until the start of the final climb. Team Sky then pressed the peloton's pace before overtaking.
The three-week race takes riders on another bumpy ride Sunday, with seven climbs in the 157.5-kilometre course from Belfort to Porrentruy.