The Australian gave his Tinkoff-Saxo team their second stage win this year by powering away in the 237.5-kilometre mountain trek from Carcassonne.
He was thrilled to have claimed his maiden victory on a day when he simply refused to be beaten. "I had the feeling that my stage truly began at the foot of the final climb and at the top, only three guys were left in the group," he said. "On the descent, Europcar's [Cyril] Gautier bridged the gap, but I just rode as fast as I possibly could on the lower slopes, created the gap and kept the pace up to the finish line.
"No-one was going to beat me today. Of course, I'm immensely happy and it's a good feeling to have a Tour de France stage win on my resume."
Vincenzo Nibali, of Italy, retained the overall leader's yellow jersey ahead of Spain's Alejandro Valverde, while France's Thibaut Pinot, who was the strongest in the intimidating ascent to the Port de Bales, moved up to third place at the expense of his compatriot Bardet.
Bardet, the AG2R-La Mondiale rider who had promised to blow the race open in the Pyrenees, was unable to sustain the pace in the climb, although team-mate Jean-Christophe Peraud could not be shaken off quite so easily.
"I had good legs, I had to attack," said Pinot, whose acceleration in the Port de Bales put all his rivals in the red. The FDJ.fr rider also holds the white jersey for the best rider under the age of 25.
Nibali leads Valverde by 4min 37sec and Pinot by 5:06 prior to two tough stages in the Pyrenees, with Peraud in fourth and 6:08 off the pace. Bardet is 32 seconds further behind.
"This is tough to take in when you were looking to attack," said the Frenchman. "I will be looking to attack tomorrow if I have the legs."
Van Garderen, the BMC rider, is 9:25 behind Nibali. "Movistar made such an insane tempo. I did not have the legs; I felt a bit empty. I'm hoping I can bounce back tomorrow," said the American.
Rui Costa, the world champion from Portugal, did not start the stage as he withdrew due to pneumonia. "He was forced to withdraw after an X-ray examination," read a Lampre team statement.
A 21-man breakaway took shape after about 60km and created a 12:30 gap that began to shrink when they hit the first slopes of the ascent to the Port de Bales, a 11.7km climb.
Astana and Movistar set the tempo of the peloton in the climb, while Rogers' acceleration in the break reduced the group to seven men. Thomas Voeckler's attack skimmed it down to four before his Europcar team-mate Gauthier burst away, although he dropped off quickly.
Rogers, the Colombian Jose Serpa and Voeckler were on their own three kilometres from the summit. That is where Pinot's team-mate Arnold Jeannesson upped the pace in front of the yellow jersey group as Bardet dropped out. Van Garderen was long gone after Valverde's Movistar team set a devilish pace at the front. Pinot finished it off in the last kilometre by dropping Valverde, Peraud and even Nibali.
However, they all came back in the descent and worked together with several team-mates and finished together. The 17th stage today is a brutal, 124.5km effort featuring four demanding climbs with a summit finish at Plat d'Adet.