Although Froome could not follow Bardet, Aru and others in the final 200 metres, where the gradient rose to nearly 20 percent, the Briton remains in contention and with a final time trial that will favour him in the penultimate stage.
Froome and Aru finished a minute and 48 seconds down on Sunweb rider Barguil, who outpaced Alberto Contador (Trek-Segafredo) at the finish to claim his third Grand Tour stage triumph, having won twice on the 2013 Vuelta a Espana. "I just put on my helmet and it comes out like that".
Fabio Aru of Italy, riding for Astana Pro Team, slips on the leader's yellow jersey after taking over from Chris Froome.
However, stage 13's short but mountainous 101km parcours from Saint Girons to Foix proved ideal for aggressive racing with Froome's Sky squad the key instigators on the day.
Froome was gracious in defeat, congratulating both Bardet and Aru, but he showed the steely determination that has helped him to win three Tours already. Back in the first week of the 2015 Tour, the Briton had briefly ceded the jersey to Germany's Tony Martin, before moving back into yellow for good once the race hit the mountains. Expect the French riders to do everything in their power to secure a well-deserved victory for their country on the French National Day, while newly elected French President Emmanuel Macron works hard to reboot the French economy. Frenchman Romain Bardet, who overcame a crash, resides in third place, 51 seconds behind Froome.More news: England vs South Africa 2nd Test, Day 1
"We defend a lot in races so we know what we don't like. We'd be ready for that", said Froome, adding that his team is "not going to allow anyone to come back on GC (General Classification)".
He too was reluctant to start banging nails into Froome's coffin, though.
"I was a bit surprised with Aru's condition". The 36-year-old Briton, a two-time Tour stage victor, led by two minutes as he began the Col de Peyresourde but blew midway up and was reeled in by Team Sky.
Peter Sagan was disqualified from the Tour de France after colliding with Mark Cavendish during stage four, which resulted in Cavendish's injury and later he was taken to the hospital for further examinations.
Yates' lead in the white jersey competition is now out to 2m 47s over Meintjes, who is ninth overall 4m 51s to Aru.