The defending champion came in at seventh position on the stage, just one second behind stage winner Michael Matthews (Sunweb). Aru, who started the day with the yellow jersey on his shoulders, lost 25 seconds to the Briton in the final effort, a 600-metre climb at an average gradient of 9.6 per cent.
Aru was out of position in the run-in to the climb and as he crossed the line his face wore a mask of pain after more than four hours on the saddle battling strong winds.
Overall, Froome now leads Aru by 18 seconds and last year's runner-up Romain Bardet by 23 seconds after the Frenchman finished five seconds off the pace. Rigoberto Uran (Cannondale-Drapac) remains fourth, six seconds behind Bardet after finishing with Froome.
Froome lost the jersey to Aru in the opening Pyrenean stage, but normal service was resumed on Saturday when he was the first of the overall favourites over the line.
"I just did not have the legs on that day, but I'd like to think that I've bounced back after two consecutive really hard days," said Froome. "This is all thanks to my team mates today. In the finale they were fantastic. Amazing, amazing job. It's an amazing feeling.
"It's still so close in the top five. Anyone within a minute is a threat," he warned.
Aru maintained that the race is still on.
"The finale was really fast, and the peloton started to split in parts. I did not have the best position and was a bit too far behind," said Aru. "I tried my best to get to the front at the last kilometre, but it did not work.
"Of course, I’d prefer to keep the leadership, but there is no major tragedy in losing it. Tomorrow is a very tough stage and also we still have a full third week with a lot of mountains. I want to recover as well as possible today and tomorrow I will keep on fighting."
Indeed, Aru losing the jersey may be a blessing in disguise, as it means the weakened Astana team can force Sky to work to defend the race lead during the tricky 15th stage in the Massif Central, which features two first-category climbs.