In a 53.5-km individual time trial heralded as a duel between Wiggins and Cadel Evans, the 32-year-old Briton came close to overhauling the 2011 Tour winner even though the Australian set off two minutes earlier.
Wiggins finally finished 34 seconds up on world time trial champion Tony Martin of Germany, with the stage winner's Sky team mate Mick Rogers of Australia in third place.
After a solid start on a winding course buffeted by strong winds, Evans slumped to eighth spot, one minute 43 seconds adrift of the Briton.
"It's always nice to beat the world champion, something to tell the kids when they're older," Wiggins told reporters.
"I've not beaten him many times in the past and it's by no means going to be the same in every time trial from now on. But to beat him by a clear margin was a huge satisfaction."
With the race now heading into the mountains on Friday, title holder Wiggins has a 38-second advantage over Martin. Rogers is third, a further 42 seconds behind.
"We'll probably have to be careful not to chase too much but this is a nice position to be in," said the overall leader.
In a year when the Tour is expected to be decided in the time trials and with Wiggins widely tipped to represent Britain at the London Olympics in the same speciality, the Briton preached caution.
"This is the Dauphine. We're still several weeks away from the Tour and that's a long time," he said.
Strong winds and a tricky early corner caused another Tour contender, triple podium finisher Andy Schleck, to crash heavily and he finished almost 11 minutes down on Wiggins in 164th spot.
"I lost a lot of skin and I went down really hard," said Schleck. "But I'm not worried for the Tour."
The race finishes in Chatel on Sunday.