Bardet made his move after eventual stage-winner Jonas Vingegaard (Jumbo-Visma) went up the road, where he eventually surpassed Nairo Quintana (Arkéa–Samsic) en route to building a 2'16" lead at the top of the overall standings.
Quintana was next to cross the line after the steady ascent of Granon, before Bardet secured third place and moved to second on the GC ahead of Geraint Thomas (Ineos Grenadiers).
In truth, it's not where the Team DSM rider expected to find himself midway through the Tour, having been on the hunt for stage wins after illness cut his pink jersey hopes short at the Giro d'Italia.
The Frenchman had earlier been dropped by Vingegaard and Pogačar (UAE Team Emirates) close to the summit of the Galibier but was able to reestablish himself on the descent towards Col du Granon, where the defending champion could not contain the Dane.
Bardet, however, thrived off the work of his teammates, and the 31-year-old was quick to credit them for his performance on a "very tough" 149-kilometre stage.
"That was very tough," Bardet told France 2 Television after the stage.
"Things began to go flat out from the Col du Télegraphe onwards and it just didn't stop.
"I had to handle my strength very carefully, but my legs responded well. It was a very good day."
"We (the team) had all taken a bit of a hit on the previous climb, the Galibier, and that definitely made a difference," he added. "So I am going to rest well tonight for sure.
"Tomorrow is another big battle in the Alps and then we'll see how things look after that. I've got a lot of fans on the roadside, but we're only halfway through."
The Tour de France continues tonight with Stage 12, a special set-piece with the summit finish to Alpe d'Huez on Bastille Day sure to bring out the best in the riders and fans. Watch from 8:55pm (AEST) on the SBS SKODA Tour Tracker and then from 9:30pm (AEST) on SBS and SBS On Demand.
