Clearly, they were having a bad day. So Froome decided to make it even worse.
Reprising the formula that carried him to victory in 2013, Froome barked an order to three teammates leading him up the punishing ascent: speed up. Shattered by the fierce uphill pace, trailing riders scattered behind them, their bluffs called and hopes dashed.
The first A-lister to crack was none other than last year's champion, Vincenzo Nibali. Sweat beading off his chin, the Sicilian was cooked. The biggest high-profile loser of Stage 10 shed more than 4 minutes to Froome, all but ending his Tour defence.
Next, Alberto Contador dropped from the by-now shriveled group of the Tour's hardiest, most pain-resistant climbers. The 2007 and 2009 champion zigzagged across the steep tarmac as Froome's trusty lieutenant Richie Porte applied yet more speed. That doomed the Spaniard's chances of adding the 2015 Tour to the Giro d'Italia title he won in May.
Two down, one major rival to go. Froome took down Nairo Quintana himself. Rising from his saddle with six kilometres (four miles) still to climb to the La Pierre-Saint-Martin ski resort, Froome accelerated away, head down, legs pumping. The bill for Quintana, who rode in third behind Froome and Porte at the top, was very costly: 1 minute and 10 seconds lost overall to the British race leader, who is now firmly in control of cycling's showcase race.
"When we got up onto that last climb and we heard the big names that were struggling and getting dropped ... I turned to the guys who were still with me at that point — it was Wouter Poels, Richie Porte and Geraint Thomas — and just said, 'Guys, come on let's on push on here. We've got them in trouble,'" Froome said.
"I couldn't have asked for it to go any better."
For his rivals, it couldn't have been much worse.
"Froome has landed a hammer blow on the Tour," said Nibali, the Astana team leader now a whopping 6:57 behind Froome overall in 10th place. "I have no more to give. I'm not even the younger brother of the Nibali from last year."
Closest to Froome is still Tejay van Garderen, the American leader of the BMC team. But he's 2 minutes, 52 seconds behind overall. Quintana, runner-up to Froome in 2013, trails by 3:09, in third. Contador slipped back to sixth overall, 4:04 behind.
"Froome rode away and showed his authority," Contador said. "I couldn't breathe. I couldn't get my legs to work. It really was a bad day."
Just as in 2013, Froome's clear superiority on the first high-mountain stage again generated questions about doping, par for the course now in cycling after the damage Lance Armstrong's era did to its reputation, even though Froome has not failed any of his hundreds of drug tests.
"I understand where the questions are coming from, (from) the history of the sport and the people before me who've won the Tour," Froome said. "But at the same time there needs to be a certain level of respect also. I mean I've worked extremely hard to get here."
There are still two more climbing days in the Pyrenees, followed by ascents in the Alps. With 11 stages still to go to the finish in Paris, Froome rightly pointed out that the race is far from done. But riding like this, it's hard to see anyone catching him unless he crashes, gets sick or has a disastrous off-day.
On Tuesday's final 15-kilometre (9-mile) climb, his Sky team also showed itself to be the strongest climbing outfit, which will help protect Froome on future ascents. With Porte second at the summit and Thomas sixth, Sky was the only team with three riders in the stage's top 10.
Asked if they have landed a knockout blow, Froome said: "I certainly wouldn't want to be in the position that some of my rivals are in."
Spectators who cycled up in the morning lined the road that snakes to an altitude of 1,610 metres (5,280 feet), in a moonscape of grey rocks and ski runs long devoid of snow. In cycling parlance, the climb is "Hors Categorie" — so tough it defies categorization.
The 167 kilometres (104 miles) ridden in 4 hours 22:07 by Froome, from Tarbes in the foothills, took the Tour through plunging valleys of great beauty with buzzards flying overhead. It also took riders past a reminder of the worst human ugliness: a concentration camp used by the pro-Nazi Vichy government during World War II to lock up Jews later deported to death camps.
The arduous climb and searing summer temperatures were a rude awakening for riders coming off their first rest day Monday, following the Tour's east-to-west swing over nine stages from the Netherlands through Belgium and across northern France.