Matthews burst clear of Greg Van Avermaet (BMC) on the steep finish to claim honours on the day. Froome crossed the line just behind in seventh place while Fabio Aru struggled up the hill and lost his yellow jersey.
The Briton now leads the general classification by 19 seconds from the Italian, with Romain Bardet (AG2R) third, 23 seconds back.
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.
Dernier kilomètre entre puncheurs, belle bataille remportée par M. Matthews ! / Tough last kilometer, great sprint for puncheurs! #TDF2017 pic.twitter.com/9VpINpTjtf
— Le Tour de France (@LeTour) July 15, 2017
Tour de France 2017 – stage 14 results (Blagnac – Rodez):
| 1 | Michael Matthews (Team Sunweb) | 4:21:56 |
| 2 | Greg Van Avermaet (BMC) | ,, |
| 3 | Edvald Boasson Hagen (Dimension Data) | +01” |
| 4 | Philippe Gilbert (Quick-Step Floors) | ,, |
| 5 | Jay McCarthy (Bora-hansgrohe) | ,, |
| 6 | Sonny Colbrelli (Bahrain Merida) | ,, |
| 7 | Chris Froome (Team Sky) | ,, |
| 8 | Daniel Martin (Quick-Step Floors) | ,, |
| 9 | Rigoberto Uran (Cannondale-Drapac) | ,, |
| 10 | Tiesj Benoot (Lotto Soudal) | +05” |
| 11 | Romain Bardet (AG2R) | ,, |
| 12 | Zdenek Stybar (Quick-Step Floors) | ,, |
| 13 | Simon Yates (Orica-Scott) | ,, |
| 14 | Jan Bakelants (AG2R) | ,, |
| 15 | Paul Martens (LottoNl-Jumbo) | ,, |
| 16 | Davide Cimolai (FDJ) | +12” |
| 17 | Nacer Bouhanni (Cofidis) | +13” |
| 18 | Simon Clarke (Cannondale-Drapac) | ,, |
| 19 | Marco Marcato (UAE Team Emirates) | +15” |
| 20 | Mikel Landa (Team Sky) | ,, |
General classification after stage 14:
| 1 | Chris Froome (Team Sky) | 59:52:09 |
| 2 | Fabio Aru (Astana) | +19” |
| 3 | Romain Bardet (AG2R) | +23” |
| 4 | Rigoberto Uran (Cannondale-Drapac) | +29” |
| 5 | Mikel Landa (Team Sky) | +01’17” |
| 6 | Daniel Martin (Quick-Step Floors) | +01’26” |
| 7 | Simon Yates (Orica-Scott) | +02’02” |
| 8 | Nairo Quintana (Movistar) | +02’22” |
| 9 | Louis Meintjes (UAE Team Emirates) | +05’09” |
| 10 | Alberto Contador (Trek-Segafredo) | +05’37” |
| 11 | George Bennett (LottoNl-Jumbo) | +06’39” |
| 12 | Pierre Latour (AG2R) | +10’56” |
| 13 | Mikel Nieve (Team Sky) | +10’58” |
| 14 | Damiano Caruso (BMC) | +11’26” |
| 15 | Warren Barguil (Team Sunweb) | +14’50” |
| 16 | Alexis Vuillermoz (AG2R) | +14’54” |
| 17 | Emanuel Buchmann (Bora-hansgrohe) | +16’52” |
| 18 | Carlos Betancur (Movistar) | +18’23” |
| 19 | Guillaume Martin (Wanty-Groupe Gobert) | +22’13” |
| 20 | Brice Feillu (Fortuneo-Oscaro) | +23’14” |
