Matthews (Team Sunweb) was the first to launch his sprint on the short but steep uphill finish in Rodez and hung on to beat Van Avermaet (BMC Racing) into second place and Edvald Boasson Hagen (Dimension Data) into third.

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Froome (Team Sky), Rigoberto Uran (Cannondale-Drapac) and Dan Martin (Quick-Step Floors) all finished one second later, but Romain Bardet (AG2R La Mondiale) crossed the line five seconds down and Aru (Astana) lost 25 seconds.
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The result means Froome moves back to the top of the general classification, 18 seconds ahead of seocnd-placed Aru and 23 seconds in front of third-placed Bardet.
Matthews, who has now won two Tour stages in his career, said: “We rode all day and when we kept the breakaway so close, I knew it was going to be hard to have a lot of team-mates in the final there because we had to ride quite hard to bring [Thomas] De Gendt back. We were still able to have two or three guys with me there in the final. It was the perfect day.
“Last time we finished on this finish, two years ago, I had four broken ribs and skin all off my body. Now to come back and win it like that on the same finish is a dream come true.”
Stage 14 took the riders on a rolling 181.5km route from Blagnac to Rodez.
Thomas Voeckler (Direct Energie), Thomas De Gendt (Lotto Soudal), Maxime Bouet (Fortuneo-Oscaro), Timo Roosen (Team LottoNL-Jumbo) and Reto Hollenstein (Katusha-Alpecin) formed a strong, five-man escape group, but Matthews’ Team Sunweb and Van Avermaet’s BMC Racing team-mates kept their lead under three minutes and a breakaway winner never looked likely.

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De Gendt survived until 12km to go and although Katusha-Alpecin launched two subsequent attacks, they were chased down and the peloton arrived at the foot of the 570m climb to the line all together.
Van Avermaet was favourite for victory after winning on the same finish at the 2015 Tour and he looked perfectly placed when he entered the final 300m on the wheel of compatriot Philippe Gilbert (Quick-Step Floors).
However, Matthews then kicked and Van Avermaet was unable to regain parity with the Australian, who made it two wins in two days for Team Sunweb, following Warren Barguil’s triumph on Stage 13.
Back down the road, Team Sky positioned Froome just off the head of the peloton going on to the final climb and he was consequently able to stay in touch with the riders challenging for stage victory.
Aru had not been so vigilant and sustained costly losses, as did Nairo Quintana (Movistar) and Alberto Contador (Trek-Segafredo), who both surrendered 21 seconds to Froome.
The Tour continues on Sunday with a 189.5km medium-mountain 15th stage from Laissac-Sévérac l'Église to Le Puy-en-Velay.