After the last hard ascent, the Briton cemented his grasp on the yellow jersey and said he sensed "that it was pretty much over" with just three racing days left.
The 143.5-kilometre ride from the southwestern town of Bagneres-de-Luchon to the ski station of Peyragudes featured three hefty ascents in the Pyrenees and an uphill finish.
Valverde, the Movistar leader who returned from a two-year doping ban this year, won his third Tour stage in a breakaway. Christopher Froome of Britain was second, and Wiggins was third, both 19 seconds back.
Wiggins faces one last test to become the first Briton to win cycling's biggest race: Saturday's individual time trial — and that's his specialty. Flat stages await on Friday and in Sunday's ride to the finish on the Champs-Elysees in Paris, and aren't expected to alter the standings.
Overall, Wiggins leads Sky teammate Froome in second by 2 minutes, 5 seconds, and Italy's Vincenzo Nibali trails in third, 2:41 back, after losing 18 seconds to them in the final ascent.
A 2-minute lead after nearly 80 hours of racing and 2 1/2 weeks might not seem like much of a margin. But in stage races like the Tour, the strategy of success for a leader is keying on his closest rivals.
Wiggins wasn't much worried about any other riders. After Nibali and Froome, his next closest challenger was Jurgen Van Den Broeck, who was 5:46 back, a deficit almost impossible to erase without a collapse by Wiggins.
Defending champion Cadel Evans of Australia, after dropping out of contention in the first Pyrenean day on Wednesday, lost more time and trailed by 9:57. Still, he rose to sixth overall, after Spain's Haimar Zubeldia lost nearly a minute to the Australian.
American Tejay Van Garderen — a BMC teammate of Evans — rose a notch, too, to fifth, and was 8:30 back.
Valverde, with tears in his eyes in the winner's circle, had a rough start to the Tour with at least three crashes. He also sensed Wiggins and Froome closing on him at the end of the stage.
"I went all out," said Valverde, who also won stages in the Tour Down Under and the Paris-Nice races this year. "When I saw there were only 700 metres left, I was really really happy".
Of his victory he said, "It erases all of the past."
One of Sky's dilemmas was exposed on Thursday: Froome entered the day clinging to an 18-second lead over Nibali, and he was looking for any chance to gain time on the Italian.
On the final ascent to the Peyragudes, Froome tried to gain time on Nibali, but also repeatedly spoke with Wiggins and even gestured with his hand for the Sky leader to come along.
"Chris encouraged me, saying 'Come on, come on,'" Wiggins said. "He's really strong ... he can win the Tour one day."
The fog-shrouded stage in the Pyrenees led the crash- and sickness-depleted peloton over three big climbs — including the Port de Bales, one of cycling's hardest — and two lesser ones.
A group of 17 breakaway riders set the early pace. Nibali joined the escapees but came to a gentleman's agreement with them and fell back. That's because the leading group knew Sky would try to chase him down — thus reducing their chance to vie for a stage win.
Nibali, too, knew that so early in the stage he wouldn't be able to hold a big gap. So after a handshake with Valverde, he drifted back to the pack to wait for chances later.
Later, Nibali's Liquigas team led up several climbs, especially Ivan Basso, the Italian veteran who was second to Lance Armstrong in his last Tour victory in 2005.
The most "panache" — the French cycling buzzword for flair — in the race came from the climbers, notably by France's Thomas Voeckler who, a day after winning Stage 16, fought hard to keep his polka-dot jersey awarded to the Tour's best climber.
As Valverde sped over the Peyrsourde pass, the last climb before a small uphill spurt to the finish, fans poured into the road — many with Spanish or Basque flags.
For bookmakers and seasoned Tour fans, Wiggins was always the pre-favourite. The main question was whether he'd hold up in the mountains. Wiggins and Sky answered that emphatically: He did.
The attacks against Wiggins in the climbs were relatively few. The biggest came from Nibali, to a lesser extent by Van Den Broeck, and less so by defending champ Evans.
From the outset, Sky has taken a methodical approach to winning the Tour. Since 2009, it set a goal of victory within five years. Wiggins has been rhythmic, not aggressive or attacking: When the best climbers were up out of their saddle pedaling in "danseuse" — dancer — position, he stayed seated, riding along behind a Sky escort or at times, leading himself.
Wiggins appears on pace to make some history: He'd become the first Olympic track champion to become a Tour winner. He took the yellow in Stage 7, and hasn't let go of it since: No rider has done that since France's Bernard Hinault held a lead from the same stage in 1981 all the way to the finish.
And only two riders have worn yellow this year: Fabian Cancellara of Switzerland had it after winning the prologue. Not since 1977 has there been only one change of the yellow jersey.
The top three — Wiggins, Froome, Nibali — haven't changed since Stage 11.
Friday's 18th stage takes riders 222.5 kilometres from Blagnac to Brive-la-Gaillarde in central France.