The AG2r-La Mondiale rider, sixth overall in the Tour last year, timed his attack perfectly near the end of the long ascent to the col du Glandon before powering away from a breakaway group on the descent.
The 24-year-old never looked back and crossed the line 33 seconds ahead of his compatriot Pierre Rolland of the Europcar team, almost two weeks after Bardet's team mate Alexis Vuillermoz won the eighth stage.
Colombian Winner Anacona of Movistar took third place, 59 seconds behind, as Chris Froome comfortably retained the overall leader's yellow jersey when he finished safely with the other top riders, 3:02 off the pace.
"It was difficult to get in the breakaway. I knew that with a late attack in the Glandon I could then take time on the others thanks to my descending skills," said Bardet, who dropped out of contention for a podium finish in Paris after a bad day in the Pyrenees.
A 29-man breakaway took shape early on and the group, featuring Bardet and fellow Frenchman Thibaut Pinot as well as polka-dot jersey wearer Joaquim Rodriguez of Spain, built a five-minute lead over the pack.
That group had been whittled down to less than a dozen midway through the ascent of the col du Glandon, a 21.7-km climb at an average gradient of 5.1 percent, after Pinot and others had dropped back.
Further behind in the yellow jersey group, Frenchman Warren Barguil attacked and was joined by Swiss Matthias Frank and Dutchman Robert Gesink.
They were caught by Alberto Contador, the only top rider who dared to attack Froome, and the four moved about 45 seconds clear of the yellow jersey group, who easily reined them in before the top of the Glandon.
Contador upped the pace again in the Lacets de Montvernier, a short but steep, serpentine climb near the finish, but Froome was never threatened.
The Team Sky rider still leads Movistar duo Nairo Quintana of Colombia by 3:10 and Alejandro Valverde of Spain by 4:09.
"We are focused on two guys at the moment: Quintana and Valverde," said Froome.
"If someone else attacks, it's their (Movistar) responsibility to look after their position on the podium."
Friday's 19th stage, a gruelling 138-km ride from St Jean de Maurienne to La Toussuire, will be the penultimate chance for Froome's rivals to prevent him securing a second Tour title.
(Reporting by Julien Pretot; Editing by Toby Davis)
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