Defending champion Chris Froome gained time on Italian Fabio Aru to win back the yellow jersey. But the stage victory went to Team Sunweb's Matthews - his second career win at the famous Grand Tour in cycling.
Australian rider Michael Matthews won a bunch sprint in the French town of Rodez to win stage 14 of the Tour de France as Chris Froome retained the yellow jersey.
The 181.5 km (112.7 miles) route from Blagnac to Rodez in southern France sees a number of third-category climbs, including a hilly finish.
Breaking from the first 10 km, Thomas Voeckler, Thomas de Gendt, Maxime Bouet, Reto Hollenstein and Timo Roosen carved out a two minute lead ahead of the peloton.
De Gendt, of Team Lotto-Soudal, was left on his own in the final 50 km, but after the chasers bunched riders together, there was another breakaway, which included German rider Niklas Arndt.
The uphill finish at Côte Saint-Pierre was always expected to come to the narrowest of margins and Matthews powered past Philippe Gilbert, John Degenkolb and Olympic champion Greg van Avermaet to win.
Froome, a three-time winner at the Tour, retook the yellow jersey ahead of Aru with 19 seconds separating the two in the general classficiation. German rider Marcel Kittel added more points to his total and retained the green jersey.