More comfortable in the Alpine habitat of the lanky man than in the previous day's crosswinds where he lost 51 seconds, Martin attacked the GC favourite group seven kilometres from the Galibier summit.
While he was caught two kilometres later, the Irishman continued to drive the pace, shelling Yates from the pack. Finishing over a minute behind Martin, the pair traded sixth and seventh places overall.
“I attacked because I wanted to test my rivals," Martin said. "I didn’t go too deep, but this doesn’t mean I wasn’t tired.
"Actually, everybody’s tired 17 days into the race, so this is turning more into a mental battle. I’m glad we left this stage behind and I got to jump one place in the GC."
But the QuickStep leader didn't have it all his own way after losing 30 seconds to Christopher Froome (Sky), Rigoberto Uran (Cannondale Drapac) and Romain Bardet (AG2R) on the descent.
“Contador was in front of me and missed a corner, leaving a gap to the others, so that was that.
"It’s already in the past and now my focus is on the Col d’Izoard, tomorrow. The war of attrition will continue there and Disco Dan is ready to dance!”
Meanwhile, Yates still leads the young rider's classification but lost a minute and thirty seconds to Louis Meintjes (UAE) who is now just two minutes and 28 seconds in the fight for the white jersey.
"It was a very difficult day, I didn’t have the best day and lost some time there in the final,” the 24-year-old said. "I didn’t really blow up mentally, I think I limited my losses ok.”
“There was quite a lot of wind about and I got shelled off the group towards the end of the final climb. I really fought a lot to stay there as I knew there was still a long way to the finish but I couldn’t do anymore.”
“We are pretty far into the tour now and I think I did really well to not lose too much time today,” Yates continued. “I went full gas on the final climb and I wasn’t strong enough today so I hope to have better legs.”