The Spaniard had actually attacked on the first categorised climb of the day, the Port de la Bonaigua, but once he had been caught he was soon in discussions with his team auto before eventually climbing in.
Defending champion Chris Froome crossed the line more than six minutes later alongside his main rivals to keep his grip on the race leader's yellow jersey. "And it'll be won and lost in those stages in the Alps".
Before the Tour's start, Froome rated this Tour campaign as his hardest.
"This is bike racing at its best", Froome said.
"(Teammate) Alejandro (Valverde) went flat out to chase that move, but it wasn't enough", Quintana added.
The British rider with Team Sky has been widely applauded and even lauded for his "panache" after pulling off a surprise downhill attack to take the yellow jersey. At the start of the stage it appeared that Movistar had selected well as the boys in blue were all over the front setting the tempo.
Despite the biblical conditions, Martin hung on as the pace of Froome's Sky squad decimated the peloton and was first to respond when Froome's Colombian wingman Sergio Henao attacked with 5km to go. The presence of Alberto Contador in the move, even though he was reported to be suffering a fever at the stage start, also heightened the tension. There were a lot of attacks on that final climb and I was hoping to gain some more time as well, but in the end I just made sure to close any gaps and not lose any time'. All the contenders were able to regroup, catch their breath and save some matches which led to the all out war in the final 5 kms of the stage.
Froome believes both Yates and Ireland's Dan Martin, the Birmingham-born rider lying third overall, can both challenge for the top three places. Rafal Majka of Team Tinkoff finished third in the race. His form has looked good, but he should rue his naïve decision to collect a water bottle on the last climb of stage eight just as Froome was making what turned out to be a stage-winning acceleration. He performed well on stage nine's summit finish, but in truth he is now riding as much for team-mate Tejay van Garderen as he is for himself. Sitting atop the leader board, he looks hard to beat.
But where so many of Britain's top riders came through British Cycling's Under 23 academy in the past, the next generation are finding their own way. Still, with the first racing block in this Tour done, there's still much more in it to unfold.
It was the second time in the last three editions of the Tour that Contador has been forced to quit due to injuries suffered in a crash.
Team Sky boss Dave Brailsford praised his rider, saying it "took some balls" for Froome to take such risks in the descent as he reached a maximum speed of about 90 kph.
Nairo Quintana (Movistar) says that he is stronger than ever for the "dogfight" to come in the Tour de France over the next two weeks.
The 23-year-old Yates is second in the overall standings, 16 seconds back and in the white jersey as the best young rider. Is he waiting again for the third week?
Froome won on Mont Ventoux on his way to overall victory in 2013, but thanked organisers for putting riders' safety first. "We're concentrating on effectiveness, there's no prize for the one who attacks the most", he said.
Team BMC needs to figure out what they are doing at the Tour. Or will Froome manage to maintain if not extend his lead from here?