After the breakaway was caught, Matthews benefitted from a strong leadout from his Orica-GreenEDGE team to claim a narrow sprint victory ahead of Nikias Arndt (Giant-Alpecin) and Alexey Tsatevich (Katusha).
The bonus seconds for winning the stage also gave Matthews the overall race lead after a day of cold and wet racing.
"I wouldn't say I was flying, but it was my first opportunity to open up in a sprint like that in a while," Matthews said.
"It was little bit foreign but I just had to take the confidence in my form at the moment."
Matthews' win was a welcome morale boost for Orica-GreenEDGE after they narrowly missed out on winning the opening stage, a team time trial.
It comes a day after Cycling Australia confirmed Matthews and Simon Gerrans would lead the national men's elite team at the world championships in Richmond, Virginia, later this month.
Despite a painful Tour de France Matthews has enjoyed a strong season, taking out a stage and briefly leading the May Giro d'Italia as well as winning the points classification at Paris-Nice.