The defending champion came seventh, one second behind stage winner Michael Matthews of Australia as 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, Briton 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.
Froome had lost the jersey to Aru in the opening Pyrenean stage, but normal service 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 5. Anyone within a minute is a threat," he warned.
Colombian Rigoberto Uran, who finished with Froome, remains fourth, six seconds behind Bardet ahead of a tricky 15th stage in the Massif Central, which features two first-category climbs.
The stage went through Carmaux, the hometown of Jean Jaures, one of the great figures of the French left and a committed anti-militarist who was assassinated in 1914 just after World War One broke out.
The one-day classics specialists had the stage victory in sight but sprinter Matthews stayed on their wheels on the last climb and outsprinted Olympic champion Greg van Avermaet, who ended up second two years after winning a Tour stage that ended in Rodez.
Norway's Edvald Boasson Hagen was third ahead of Belgian Philippe Gilbert, who launched his sprint too early and cracked 150 metres from the finish line.
"It's a dream come true," said Matthews, whose Team Sunweb claimed their second stage wins in as many days after Frenchman Warren Barguil claimed stage 13 on Bastille Day.
"We're room mates, so it's two wins for one room," said Matthews.
(Reporting by Julien Pretot,; Editing by Ed Osmond)
Share
