As Kwiatkowski came into sight, however, Froome attacked to join his Polish team-mate and his efforts initially split the group – Yates among those behind the gap – before it came back together on the descent.
The lead in the yellow jersey group repeatedly changed on the descent, with several riders giving it a go, but the gap to the front quartet held around the two-minute mark.
Uran got a small gap but was caught at the bottom of the descent, while Martin took advantage of a lull at the bottom to attack too.
With Froome the only rider in the GC group with a team-mate for company, the defending champion repeatedly tested Aru, before Yates bridged across to Martin.
Aru would not be beaten, however, and as Barguil was outsprinting Contador, Quintana and Landa to claim his first Tour de France stage win – becoming the first Frenchman to win on Bastille Day since 2005 – Aru and his rivals were all together.
Martin and Yates’ attacks earned them nine seconds, but Aru still leads by six seconds overall from Froome.
Tour de France 2017: stage 13 – result
1) Warren Barguil (FRA) – Team Sunweb – 2.36.29hrs
2) Nairo Quintana (COL) – Movistar – ST
3) Alberto Contador (ESP) – Trek-Segafredo
4) Mikel Landa (ESP) – Team Sky +2”
5) Simon Yates (GBR) – Orica-Scott +1.39
6) Daniel Martin (IRL) – QuickStep Floors – ST
7) Michal Kwiatkowski (POL) – Team Sky +1.48
8) Chris Froome (GBR) – Team Sky – ST
9) Fabio Aru (ITA) – Astana
10) Rigoberto Uran (COL) – Cannondale-Drapac
1) Fabio Aru (ITA) – Astana – 55.30.06hrs
2) Chris Froome (GBR) – Team Sky +6”
3) Romain Bardet (FRA) – Ag2r-La Mondiale +25”
4) Rigoberto Uran (COL) – Cannondale-Drapac +35”
5) Mikel Landa (ESP) – Team Sky +1.09
6) Daniel Martin (IRL) – QuickStep Floors +1.32
7) Simon Yates (GBR) – Orica-Scott +2.04
8) Nairo Quintana (COL) – Movistar +2.07
9) Louis Meintjes (RSA) – UAE Team Emirates +4.51
10) Alberto Contador (ESP) – Trek-Segafredo +5.22