With BMC's Greg Van Avermaet, who defended the yellow jersey in such style on stage 10, struggling off the back of the peloton on the Col du Pre - the second of the day's two uncategorised climbs - the race for yellow was on and it was Movistar's Alejandro Valverde who blinked first with a long-range attack.
Sky teammate Geraint Thomas is second over all, 43 seconds behind van Avermaet, meaning the team has two viable options to claim the yellow jersey over the second week of the three-week Tour.
The general classification broadly remained as it was with van Avermaet extended his lead to 2min 22sec when the group containing the heads of state including Chris Froome (Sky) rolled across the finish 3min 23sec after the stage victor.
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But Sky kept their powder dry until Thomas launched his move.
Froome himself would subsequently follow a move from UAE Team Emirates rider Dan Martin and finished third, crossing the line just behind Dumoulin, both riders 20 seconds behind Thomas.
"I'm feeling good and optimistic about the upcoming stages", the four-time champion said on Monday, the Tour's first rest day.
"We were low on numbers, so it was instinct when I went".
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Thomas attacked six kilometres from the top of the final climb of the 108.5km stage from Albertville, overhauling rival Tom Dumoulin and then pushing on to catch former team-mate Mikel Nieve, who was looking to win the stage out of the breakaway.
"Dumoulin is right up there on the GC now, we couldn't give him too much room and obviously he is someone who can TT at the end of the Tour as well so we are going to have to keep a close eye on him", Froome added. Jakob Fuglsang of Astana was next at 3:12.
This stage was the first of three days in the Alps following the relatively flat legs of the first nine days.
With van Avermaet not a specialist climber, Thomas could potentially take yellow today when the Tour resumes with a huge 158.5km mountain stage from Annecy to Le Grand Bornand. To wear the yellow jersey is always a massive honour.
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Sprinting standout Mark Cavendish, meanwhile, finished far behind and missed the time limit, ending his Tour.