Pinot attacked a reduced group of favourites with 6.2km to go on the 11.7km climb, with no-one setting off in pursuit due to his more than two-minute deficit on GC.
The Frenchman was able to extend his gap out to 18 seconds over a group of Alejandro Valverde and Nairo Quintana (Movistar), Miguel Angel Lopez (Astana) and Enric Mas (Quick-Step Floors) as well as Yates.
That group continued to attack each other up the climb, but no-one was really able to make big inroads as the kilometres ticked down.
A late attack from Lopez wasn't enough to stop Pinot soaring to victory on the stage, with the Colombian rolling in second with a small gap to Yates who made a late dash ahead of the Movistar duo to extend his lead by six seconds over Valverde.
How it happened
A third consecutive summit finish welcomed the riders of the Vuelta a España on stage 15, with a brutal finish to the top of Lagos de Covadonga.
With a category three and two category one climbs along the way, a breakaway would have eyed their chances at making it to the finish if the GC teams were content to let them establish a gap, and 12 men took the opportunity early on.
It took around 40km of the 178.2km stage for them to go clear, with Ivan Garcia (Bahrain-Merida), Imanol Erviti (Movistar), Ben King (Dimension Data), Pierre Rolland (EF Education First-Drapac), George Bennett, Danny van Poppel (LottoNL-Jumbo), Tao Geoghegan Hart (Team Sky), Bauke Mollema, Fabio Felline (Trek-Segafredo), Valerio Conti (UAE Team Emirates), Nick Schultz (Caja Rural), and Nicolas Roche (BMC Racing) making up the group.
They established a maximum gap of around five minutes, but that began to deteriorate over the climbs, though they still carried around three minutes as the likes of Van Poppel and Roche dropped of in the final 40km.
Astana led the peloton as they tried to set things up for Lopez, with the only drama before the climb coming as Michal Kwiatkowski (Team Sky) crashed and looked injured after falling with Alexandre Geniez (Ag2r La Mondiale).
In the final 20km on the approach to the climb, the break began to really lose their cohesion, and it was Ivan Garcia who decided he'd had enough and broke clear.
He held off his former breakaway companions and still held around 2-30 as he reached the final 12km climb alone.
With the other breakers then all caught by the shrinking peloton on the climb, Garcia held just 25 seconds with 8.5km left to climb, with Astana still driving the pace.
The Spaniard was eventually caught just 500m later, with the favourites then set to battle it out for the stage as well as time in GC.
Lopez was the first to hit out with 7.7km left, with the numbers of Movistar setting off in pursuit. It was short lived though as he was caught just a kilometre later, but the injection of pace thinned out the leading group.
Thibaut Pinot then had a go with 6.2km remaining, with no immediate response from the others thanks to his 2-46 deficit overall.
Shortly after race leader Yates then set off in pursuit, immediately gapping the other favourites. Alejandro Valverde tried to pick it up to help Quintana get back to the red jersey, and was eventually able to make contact with 5.3km to go.
Pinot continued to gain and moved to 16 seconds up the road, with the attacks continuing to fly behind with Yates making a move that cut down the group to four with Enric Mas as well as Lopez and Quintana involved. Valverde was able to work his way back to that group shortly after.
Lopez then made a move again with 2.1km to go, with no interest from anyone in taking up the chase again, and he was able to get a decent gap up the road.
It wouldn't be enough to stop Pinot, who by now was assured of a stage victory on the Vuelta's famous climb, but the Colombian was able to make a small time gain, crossing the line two seconds ahead of race leader Yates who made a late attack, with Valverde a further two seconds down. Quintana arrived a further two seconds back, with Steven Kruijswijk (LottoNL-Jumbo), having made it back after getting dropped with a few kilometres to go, beating him to the line.
The Vuelta a España will head into its second rest day on Monday, with an individual time trial to come on Tuesday's stage 16.
Vuelta a España 2018, stage 15: Ribera de Arriba to Lagos de Covadonga (178.2k)
1 Thibaut Pinot (Fra) Groupama-FDJ, in 5-01-49
2 Miguel Angel Lopez (Col) Astana Pro Team, at 28s
3 Simon Yates (GBr) Mitchelton-Scott, at 30s
4 Alejandro Valverde (Esp) Movistar Team, at 32s
5 Steven Kruijswijk (Ned) LottoNL-Jumbo, at same time
6 Enric Mas (Esp) Quick-Step Floors, at 34s
7 Nairo Quintana (Col) Movistar Team
8 Rigoberto Uran (Col) EF Education First-Drapac, at 1-25
9 Emanuel Buchmann (Ger) Bora-Hansgrohe, at 1-33
10 Ion Izagirre (Esp) Bahrain-Merida, at 1-49
Overall classification after stage 15
1 Simon Yates (GBr) Mitchelton-Scott, in 59-11-18
2 Alejandro Valverde (Esp) Movistar Team, at 26s
3 Nairo Quintana (Col) Movistar Team, at 33s
4 Miguel Angel Lopez (Col) Astana Pro Team, at 43s
5 Steven Kruijswijk (Ned) LottoNL-Jumbo, at 1-29
6 Enric Mas (Esp) Quick-Step Floors, at 1-55
7 Thibaut Pinot (Fra) Groupama-FDJ, at 2-10
8 Rigoberto Uran (Col) EF Education First-Drapac, at 2-27
9 Ion Izagirre (Esp) Bahrain-Merida, at 3-03
19 Emanual Buchmann (Ger) Bora-Hansgrohe, 3-15
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