Only the category 4 Côte de Madiran and Côte d'Anos are any lumps of note across the route and the finish in Pau, a popular tour destination, is flat although the last two kilometres are tricky with a roundabout onto boulevard Recteur Jean Sarrailh, and a sharp left onto avenue Jean Mermoz; before a second roundabout onto the boulevard Champetier de Ribes and a sharp left onto rue Michelet/rue du Maquis de Béarn, and the finish line by place de Verdun.
He took third place behind Colombian Nairo Quintana and Ireland's Dan Martin, but gained time over Froome, Dumoulin and fourth-placed Primoz Roglic.
"It was squeaky bum time".
"I can thank Greipel", he said.
Froome finished eighth, 1:35 behind, and dropped from second to third overall, a distant 2 minutes, 31 seconds behind Thomas.
Ominously, Thomas's poor performance benefited Primoz Roglic, victor of Friday's stage, who went on to win the Swiss race overall. "Hopefully I make it home in time for that".
"I was the first rider to come down the descent and one of the gendarmes grabbed my arm as I was passing", Froome said.
"I think we're in a brilliant position with G in the yellow jersey", Froome told NBC TV as he rolled past the line.
Asked if the outcome means Sky is now all riding for him, Thomas said: "I guess so".
With some riders still clambering towards the finish line, a gendarme mistook the four-time victor for a fan and asked him to stop, causing Froome and his bodyguard to crash. 'But I still felt strong and had the energy to finish the race on a high'.
Three homicides in five days at BART stations an ‘anomaly,’ official says
Police stopped the train at Pleasant Hill station , where officers boarded and arrested Cowell without incident. Court documents show a restraining order was filed in April 2016 by Kaiser Foundation against Cowell.
The collision occurred on Wednesday during the 65-kilometer stretch from Bagneres-de-Luchon and Saint-Lary-Soulan.
'I went through some hard moments in the first part of this Tour and lost some time, ' said Quintana, who is fifth overall.
Measuring 16 km at an average gradient of almost nine percent, organizers rated the Col du Portet as the second-hardest climb in Tour history after Mont Ventoux.
Estonian rider Tanel Kangert launched an early solo breakaway and was first over the Montee de Peyragudes, the opening climb.
Tangert was alone in the lead until halfway up the Col du Portet, when Quintana caught him and surged ahead.
The incident comes a day after police used tear gas to disperse a farmers' protest that had blocked the road with bales of hay.
Demare was set up in impressive fashion for a sprint finish by his Groupama team, who worked hard in the final kilometres to make sure Slovakian sprint king Peter Sagan's chances were limited.
Only two challenging stages remain - a lengthy leg through the Pyrenees including three major climbs, then a technical individual time trial - before the mostly ceremonial finish on the Champs-Elysees in Paris on Sunday.