The Australian burst from the pack to win ahead of Greg Van Avermaet (BMC Racing) and Jasper Stuyven (Trek-Segafredo), and paid tribute to Australia's last winner of the race, Simon Gerrans, who will retire from the sport in the coming weeks.
This year has been a rocky one for Matthews, who has suffered injury, illness and bad luck ever since his first race of the season in February.
The 27-year-old has been chasing form and fitness all year, but after pulling out of the Tour de France due to illness, he regrouped and claimed a stage win and took second overall at the BinckBank Tour in August.
On Friday he was back to his best, timing his dash to the line perfectly and winning his first one-day WorldTour race in the process.
"It's been a really rocky start to the year. I'm just happy that I've been able to turn it around in a positive way for the second half of the season," he said at his winner's press conference.
"I could have sat up and thought about giving the rest of the season a miss, but the team kept being positive for me. My wife and I really put a lot into the second half of this season. We sacrificed a lot in order to make sure that I was good enough for these races, so that I could perform where I should be.
"It's really quite emotional to get this win. It's really something special. It's not just another ticked box. I'm super-happy to win here because it's just such a beautiful race."
In an exclusive podcast with Cyclingnews, recorded two days before Quebec, Matthews gave a frank and honest account of his year to date, and opened up about the physical and mental battles he has overcome in order to return to the top of the sport.
On Friday he praised his wife for her support through the difficult moments of injury and doubt.
"The whole season has been so rocky. Last year was such a good season and I wanted to step up again this year, but my wife has been my biggest helper this year. I couldn't have done what I'm doing now without her. She has always backed me. She was always pushing me and telling me that it would turn around. It's amazing to have someone like that by your side, even when the world seems to keep throwing things at you."
Matthews also took a moment to commend Simon Gerrans, who retires later this year. The BMC Racing rider was the last Australian to win in Quebec – in 2014 – before going on to win a few days later in Montreal.
The two riders, who rode as teammates at Orica, famously fell out during the 2015 Worlds, and Matthews left Orica at the end of the 2016 season, with Gerrans also moving on a year later.
Time has healed some of those wounds, to some extent, and Matthews has tried to rebuild the bridges between two riders who are, by their own admissions, very different characters.
When asked whether he could repeat Gerrans' 2014 Canadian exploits and also win in Montreal, Matthews replied: "The year he did that he was really good. It's going to be super-hard to do that, but I've really studied the way that he did it. Even today with the team that we have here, we tried to do the same plan that they tried to do at GreenEdge to help Simon win in 2014.
"It's sad to see Gerrans go, actually. He's someone that I looked up to my whole career. We're similar riders, too, and he's had an amazing career. He should be really happy with what he's done, and I wish him the best for after his career.
"For me, Montreal is a different race, but it also suits me. We'll have to wait and see."
With Gerrans set to leave the sport, Matthews will take up the mantle as Australia's leading rider outside of GC racing, and pure sprinting. He still has some way to go in order to match Gerrans' palmarès, but if Quebec is anything to go by, Gerrans' heir is very much back to his best.
"This is actually massive. I've won a stage in each of the Grand Tours. I've won a stage in almost every week-long stage race, and worn nearly every leader's jersey expect for at the Tour de France.
"This means a lot to me, and it was the first thing that I thought about when I crossed the finish line. One thing that was missing from my palmarès was a Classic, and so I'm super-happy to get it."