Britain's Bradley Wiggins is 38 seconds ahead overall after he fended off mid-stage attacks by Australian Cadel Evans to finish in the main pack. Germany's Tony Martin is second and Australian Mick Rogers third, 80 seconds off the pace.
As the race reached flatter roads towards the end of an ardous day's trek through the Alps, Vichot powered away from a break of eight riders to seize the biggest win of his career.
Spain's Egoi Martínez was second, 26 seconds adrift, and Kazakh Dmitriy Fofonov third in the 186.5-km stage from Saint-Trivier-sur-Moignans.
"There are three tough mountain stages this weekend and this was the one I wanted to go for, the kind we like in my FDJ-Big Mat team," Vichot told reporters.
"There wasn't much collaborating within the break so I opted to go for it alone even though I thought I was the fastest sprinter in the move.
"It's a big step forward for me. I asked the team if I could ride more important races this season to try and show what I could do and today that's paid off."
Vichot said victory represented a welcome break from a run of poor results for his team.
"We've had a lot of minor problems from the start of the season that have combined to make it harder for us to win," he explained.
"That happens in all teams but we're not a big team like Sky so when one or two of our leaders aren't in great shape, you can tell very quickly," added Vichot.
"I want to go to the Tour de France (next month) and try and get a stage win."
Saturday's ascent of the infamously steep Col de Joux Plane en route to Morzine is Wiggins's major remaining obstacle as he bids to claim a second straight victory in France's third biggest stage race.
The Dauphine ends on Sunday in Chatel.