The Australian, with three Vuelta and two Giro d’Italia stage wins to his name, outsprinted his breakaway companions after 197km from Escaldes-Engordany, Andorra, benefiting from the support of two of his Orica-Bike Exchange team mates.
World champion Peter Sagan (Tinkoff), who reclaimed the green jersey for the points classification from Briton Mark Cavendish, took second place and Norway’s Edvald Boasson Hagen (Dimension Data) finished third.
Matthews missed the 2014 Tour after sustaining injuries in training and last year, he abandoned after breaking four ribs.
“And this year already I had crashed twice. I was almost giving up on this race, thinking maybe the Tour de France is not for me,” he said.
Briton Chris Froome (Team Sky) retained the overall leader's yellow jersey after finishing safe in the main peloton 9:39 off the pace.
“The start was pretty full on, there was a lot of work for my team mates to control the race,” said Froome.
“But it was pretty straightforward from there. However, it’s a good day to tick off.”
The stage got off to a nervous start on the category-one climb to the Port d’Envalira, as riders were keen to win places in the day's breakaway which took its final shape after about 60 kilometres.
