The plan could be a double-edged sword, though, now that Froome's team mate Mikel Landa has emerged as a potential Tour winner himself.
Italian Fabio Aru, who kept his cool despite quickly finding himself without any team mates to help him, retained the leader's yellow jersey and finished in the group of favourites with Froome and third-placed Romain Bardet, all 1:48 seconds off Barguil's pace.
"I was always composed," said Aru, whose Astana lieutenant Jakob Fuglsang abandoned on Friday after sustaining wrist and elbow fractures in a crash two days ago.
A day after Froome showed a rare sign of weakness on the final slope, Team Sky sent Spain's Landa in front when twice champion Alberto Contador attacked early on.
Landa finished fourth behind Contador and Colombian Nairo Quintana, who is back in contention in eighth place overall, 2:07 behind Aru.
"Beating Contador is something huge for me because he's always been my idol," said Barguil.
"I had great legs today after a tough stage yesterday."
Aru leads Froome by six seconds overall with last year's runner-up Bardet in third place, 25 seconds behind the race leader and Colombian Rigoberto Uran in fourth, a further 10 seconds back.
Landa is now fifth, 1:09 behind Aru, and Team Sky's management will need to make clear who the leader is after the Spaniard, whose contract expires at the end of the year, finished ahead of Froome on Thursday.
The situation is reminiscent of 2012, when Bradley Wiggins won the Tour but came under pressure from Froome, who had to be restrained by Sky's team managers on a mountain stage when he appeared stronger than his leader.
Asked if he felt stronger than Froome, Landa said: "I don't think so, Chris has won three Tours de France."
PERFECT POSITION
Froome appeared to struggle in the last of three climbs in the punchy 101-km stage, but he still managed to attack his rivals in the final part of the Mur de Peguere, a punishing 9.3-km ascent at an average gradient of 7.9 percent.
"Landa is a real threat now for the overall title in Paris, it's a great card for us to play, especially since Astana don't have the numbers to control the race," said Froome.
"I'm very happy. That's a perfect position for us especially going into these (tough) stages coming up, he could be a card for us to play again."
Sky never had to chase on a day of danger for them as Landa, who appears to be in top shape despite riding the Giro d'Italia in May-June, was in front with Contador.
The leading duo were caught by Barguil and Quintana just before the summit of the Mur de Peguere and the Frenchman, who strengthened his grip on the polka dot jersey, proved the stronger sprinter.
In the final descent, Uran, Bardet and also Ireland's Dan Martin and Froome all attacked as they tried to leave Aru behind, but the Sardinian maintained his composure and stayed close to his opponents for the yellow jersey.
"At some point I stopped counting the attacks," said Aru.
Saturday's 14th stage, a 181-km ride from Blagnac to Rodez, suits the breakaway specialists.
The overall contenders are expected to be in proper action again next Wednesday and Thursday in the last two mountain stages in the Alps.
(Reporting by Julien Pretot; Editing by Hugh Lawson)
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