The AG2R rider and peloton traversed seven categorised climbs, including the Col du Glandon and Lacets de Montvernier, to finish solo in Saint-Jean-de-Maurienne.
"I am a happy man, yes, but I still can’t believe it. It was a difficult," Bardet said.
"There were a lot of hopes pinned on me from the start of the Tour de France. Perhaps people thought I should have been doing better earlier, so we had to be very strong mentally.
"I always had the support of the team, and we are a bunch of friends.
"But yesterday, I was flat. I was close to dropping everything. I thought, ‘Three months preparing for the Tour, and you’ve hit the plateau.’
"But then I said to myself, ‘Come on, you don’t give up. You never know what can happen.’
“I was really good today. I was ahead, and courage paid off.”
The victory was the second in this year's Tour for the French after Bardet's team-mate Alexis Vuillermoz's Stage 8 win on the Mûr-de-Bretagne. It sent the home fans wild with celebrations.
Second was another Frenchman, Pierre Rolland (Europcar), while Movistar’s Winner Anacona rounded out the podium in third.
The rest of the original break dominated the stage top 10 as the key contenders stayed together to the finish despite several attempts to rattle race leader Chris Froome (Team Sky).
The unchanged general classification sees Froome continuing to lead the Movistar pair of Nairo Quintana and Alejandro Valverde.
The 186.5km stage from Gap opened up with a large 29-rider breakaway group, which carried on together until it split after the intermediate sprint and before the massive climb on the Col du Glandon.
Mountains classification leader Joaquim Rodriguez (Katusha) led Jakob Fuglsang (Astana), Jan Bakelants (AG2R), Anacona (Movistar), Damiano Caruso (BMC), Thomas De Gendt (Lotto-Soudal), Thomas Voeckler (Europcar), Ruben Plaza (Lampre-Merida), Andrew Talansky, Dan Martin (Cannondale-Garmin) and Jan Barta (Bora Argon 18) in that group.
The 21km climb did what it was designed to do; separate the pretenders from the contenders and reduce the number of riders in the Rodriguez-led break and the Froome-led chase.
The time gap fluctuated but the break held three minutes with 50km to go and the same again at 40km when the stage cracked open for the entire peloton after an attack by Alberto Contador (Tinkoff-Saxo) and Vincenzo Nibali (Astana) from the yellow jersey group.
Both of the pre-race favourites created some gaps to Froome but madcap hairpin descending brought proceedings together ahead of the final climb over Lacets de Montvernier.
While the general classification favourites were toying with each other Bardet made the critical decision to escape the clutches of Rodriguez and the rest of the lead group on the Glandon.
The next uphill challenge for the peloton was the picturesque 3.4km long Lacets de Montvernier climb, used for the first time in Tour history.
There, Bardet held a three-minute lead on the yellow jersey group of Froome, while a strong chase came from Fuglsang, Anacona, Rolland and Bob Jungels (Trek Factory Racing).
After an exhilarating descent of Lacets de Montvernier Bardet drove as hard as he could on the flat road to Saint-Jean-de-Maurienne in the final few kilometres and managed to finish 33 seconds ahead of Rolland.