Greg van Avermaet showed powers of perseverance to hold off Peter Sagan and win the 13th stage from Muret to Rodez.

Mark Cavendish thought he had a slim chance of a 27th stage victory on the 198.5-kilometre route, but the concluding climb of Saint-Pierre was 570 metres long at 9.6 per cent, which is the same average gradient as the punishing Mur de Huy.

It was more suited to the likes of Sagan (Tinkoff-Saxo) and John Degenkolb (Giant-Alpecin), but it was Belgian Van Avermaet who claimed his first Tour stage success.

Sagan looked to be rounding the BMC Racing rider in the finishing straight, but Van Avermaet gritted his teeth to ensure the Slovakian's search for a first stage win in two years goes on.

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There was small consolation for Sagan, who retained the points classification leader's green jersey after Andre Greipel (Lotto-Soudal) temporarily dislodged him from the lead at the day's intermediate sprint.

Chris Froome (Team Sky) finished sixth, seven seconds behind, to maintain his overall advantage of two minutes 52 seconds over second-placed Tejay van Garderen (BMC Racing).

Nairo Quintana stayed third, 3:09 adrift as the top of the general classification remained unchanged, with Geraint Thomas (Team Sky) still fifth, 4:03 back.