Matthews was one second faster than Tom Bohli of Switzerland on the 4-kilometer (2-1/2 mile) route around Fribourg. Primoz Roglic of Slovenia was third.
After a stellar 2017, when he won two Tour de France stages and the green jersey as most consistent finisher, Matthews had a low-key European spring season.
The Team Sunweb rider told Swiss broadcaster RTS it was a “massive relief” to get his first win.
The six-day race through Switzerland’s French-speaking region continues Wednesday with a 166-kilometer (103-mile) ride from Fribourg to Delemont. It includes three category 2 climbs.
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