The Orica-Scott rider was on the right end of the split in the finale whereas Martin and Meintjes missed the move to concede 51 seconds. Yates leapfrogged Martin into sixth by just one second ahead of the Alps double header to Serre Chevalier and the Col d'Izoard.
The 24-year-old singled out teammate Jens Keukeleire for praise, adding the team support has been crucial to his success thus far in the Tour.
“I felt good and I had good legs again today. I’ve been getting better with each day," said Yates after he finished in 14th place. "The team did a fantastic job today, they were always around me and had me in the right position at all of the crucial moments so I didn’t have to do a lot at all. Jens Keukeleire did a really fantastic job for me when it really started to split there in the wind and once I made that front group I was in a good position.
"In the end it was a perfect day."
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While Nairo Quintana at 6:16 minutes to yellow jersey holder Chris Froome (Team Sky) in tenth place is out of contention for the overall podium, Yates at 2:02 minutes is within reach of the top three. Last year, sports director Matt White directed Adam Yates to fourth place overall and the white jersey. With four crucial stages to come, White explained the team has executed its plans to remain in contention for its pre-Tour aims.
"We had good information and we knew where we had to be and when. The whole team did a great job of keeping Simon safe and in the right place as you could see," said White. "This Tour de France has shown that everything can change in a second and with the top riders so close on the GC, we are happy to be up there fighting amongst them."
With Martin just one second off Yates' sixth place, the Briton's lead in the white jersey classification sis far healthier with Meintjes at 3:58 minutes and Pierre Latour in third at 12:30 minutes. Barring disaster in the final week, Yates will be making at least one trip to the Paris podium but Orica-Scott will be aiming to make it two with a strong showing in the Alps starting Wednesday.