Although there was no reward for his effort, Yates will head into the second rest day with a comfortable buffer in the white jersey classification and just over 90 seconds off a podium place.
The transitional stage 15 through the Massif Central promised anything but racing and lived up to expectation as yellow jersey holder Chris Froome (Sky) suffered a mechanical just moment after AG2R-La Mondale took advantage of Romain Bardet's local knowledge.
Despite the drama, the GC riders, bar the fading Nairo Quintana, were all together on the approach to the category 4 Cote de Saint-Vidal were Yates made his move. Sky's Mikel Landa brought Yates back to the bunch before Dan Martin made his late move to steal precious seconds.
Yates finished the day ahead of Froome in 27th place and over six minutes down on stage winner Bauke Mollema (Trek-Segafredo).
"I like to race aggressively and today was one of those days I could do that," Yates said. "I was trying to sneak away, like I did the other day, and get some seconds. It didn't work out, but that's OK, it's worth trying and I gave it a go."
With the closest battle for the general classification in race history at this stage of the Tour, 24-year-old Yates is looking to take time whenever and wherever he can in the final week.
"I had good legs and you look at how close the race is. I could have possibly gained 10 seconds, 15seconds maximum, but I think every second will count when it comes to Paris," he added.
Sports director Matt White added that he is been pleased with Yates' showing on his first attempt at riding GC in July and is looking forward to the decisive third week.
"Another very exciting stage today, especially in the final. What we saw today was the top seven or eight guys have increased their gap on the group. The big loser today was Nairo Quintana who fell out of the top ten," White said in the team's Backstage Pass video. "Simon has certainly shown he is one of the best climbers in that very elite group and even put in a couple of attacks in the final. We go into tomorrow, our second well-deserved rest day and [we have] some exciting stuff coming for the last part of the Tour."