Although Bardet was defeated, he certainly caught the imagination with an inspired and aggressive ride, and moved into third overall, 21 seconds off Chris Froome's lead.
The AG2R La Mondiale team sent Jan Bakelants, Mikaël Chérel and Ben Gastauer up the road in the day's main break before Bardet joined forces with Fabio Aru (Astana) and bridged across.
The French team set a furious pace at the front of the break, going toe-to-toe with Team Sky, who were leading the chase for Froome. At the foot of the final climb the AG2R-led break had three minutes over the bunch when Bardet exploded off the front with 10 kilometres to go.
He was on his own for less than a kilometre when Pinot painfully dragged himself up to his rival's wheel. The FDJ rider was less of a threat on GC, while Bardet was still the virtual leader on the road having started the stage less than two minutes down on Froome. It meant that Bardet was forced to set the pace for the majority of the climb and when he attacked Pinot once more with three kilometres to go he couldn't shake his companion.
"It was exceptional," Bardet said of his team's performance after they took the race by the scruff of the race and dictated proceedings.
"Two years ago we did the same in the Dauphine with Jean-Christophe Peraud and Alexis Gougeard and today it was with Ben, Mickaël and Jan. It was incredible. They gave it all from me and I tried to give my best on the last climb."
Bardet appeared to be racing on pure instinct, a characteristic that makes him stand out in the mountains. He admitted that the fact that he was in the hunt for the stage win but also in contention for the leader's jersey made his task all the more difficult.
"There was no tactic. I've not won yet this year but I wanted to take a win here, especially at the Dauphine, but when you have the win in mind it's hard to think about the overall. I didn't have a choice and that's maybe why I don't have the win or the GC."
Bardet also bore no grudge in relation to Pinot, who jumped him at the line after Bardet had done the majority of the work.
"That was normal from Pinot. He was far down on the overall classification so he didn't have to do the same work at the head of the race. I had the race on my shoulders and I tried to do my best but it wasn't enough to win or take the yellow jersey."
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