Chris Froome picked Rigoberto Uran as the biggest threat to his bid to win a fourth Tour de France after conserving his lead as won Thursday's 18th stage.
Froome finished fourth, giving up four bonus seconds to but putting two more into Uran.
Bardet moved up to second at 23sec with Uran dropping to third at 29sec in what has now become a three-way battle for the Tour title.
But with Saturday's 22.5m time-trial in Marseille the likely last chance to take time, Froome is feeling confident.
"Definitely Rigo is still probably at this moment my biggest threat for the time-trial in Marseille from the GC group," said Froome.
"He's the next strongest in the time-trial. He's only 29 seconds behind me so I imagine he'll be the guy to look out for."
- 'Alps the toughest' -
In his previous Tour victories, Froome had always struggled on at least one Alpine stage as rivals fought back against him.
Those years, though, he had a much greater advantage. This time, he couldn't afford to give up anything.
"I'm happy to have passed the Alps without problems this year," said Froome, 32.
"The Alps are always the toughest for me. Now I'm looking forward to the time-trial in Marseille."
Frenchman Barguil won his second stage of the Tour on the imposing Col d'Izoard, having also tasted success on Bastille Day, the French national holiday, on stage 13.
Colombian Darwin Atapuma finished second, 20sec behind Barguil, with Bardet winning the sprint for third against Froome and Uran, thus taking the last four bonus seconds on offer.
He and Uran at least kept their overall hopes alive, which was more than could said of .
The Italian held the yellow jersey for two days last week, having also won stage nine, the first summit finish of the Tour.
But he said he was handicapped by bronchitis as he cracked and lost more than a minute, dropping from fourth to fifth overall at 1min 55sec, as Froome's Sky team-mate Mikel Landa jumped a place to fourth at 1:36.
"Physical problems are part of sport and you have to accept it," said Aru.
"And fifth place isn't something to be scoffed at."
- 'Living in my dream' -
It was a thrilling battle on the final hors category climb at the end of the 179.5km Alpine 18th stage from Briancon to the Col d'Izoard.
Atapuma was part of an original 54-man breakaway that splintered over the two huge climbs of the day.
He reeled in Kazakh halfway up the Izoard climb while the peloton led by Bardet's AG2R team, at one point eight minutes back, started to close in.
Barguil made his move with 6km to go but still had two minutes to make up on Atapuma, catching him with 1.4km left and dropping him inside the final kilometre to win the first ever stage finish on the Izoard.
"I'm just living in my dream at the moment, it's just crazy," said Barguil.
"After a lot of bad luck I've shown finally my real potential to everybody."
Barguil, who had already sewn up the king of the mountains polkadot jersey earlier in the day, leapt above two-time former winner Alberto Contador into ninth overall.
"I'm still in the clouds, I've left the earth," said Barguil.
"It's an exceptional day, I never have imagined I could win on the Izoard."
Behind Barguil, Bardet launched an attack 3km from the finish but Froome and Colombian Uran stuck to him like glue.
Briton Froome attacked next but couldn't stay clear and once they hit the final kilometre it was a battle of wills to the line at a vertiginous 2,360-metres above sea level.
Uran may have given up a few seconds, but is widely regarded a better time-trialist than Bardet, who is only six seconds ahead.
"I thought I was going to suffocate when I crossed the line, it was hugely mental," said an exhausted Bardet.
"I gave absolutely everything."
Source: AFP
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