Matthews (Sunweb) shot to the front in the final kilometre sprint to the line after he was led out by teammate Nickias Arndt.
The 26-year-old Canberran beat out Peter Sagan (BORA-hansgrohe) and John Degenkolb (Trek-Segafredo) in a sprint to the line and took the yellow jersey from BMC's Stefan Kung.
Matthews hailed the performance of Arndt in helping get him over the line in first after he struggled on the final ascent.
"I struggled a little bit on the climb. I wasn't climbing so well today but it was good enough," Matthews said.
"I saw that I had a teammate there with Nikias Arndt and that gave me massive motivation because I knew he could do a really big pull and that made it perfect for me to do my sprint at the right time, not like last year when I got boxed in during the Tour.
"It's nice to get the win that I really wanted last year. It will be nice having the leader's jersey tomorrow. The team won the Giro d'Italia so I guess they know how to ride on the front now."
Lurking just behind Matthews in the overall classification is his Sunweb teammate and Giro d'Italia winner Tom Dumoulin, who is only 10 seconds off the pace and continuing to show good form in the lead up to the Tour de France.
Stage 4 runs 150km from Bern to Villars-sur-Ollon as the Tour enters the mountains before finishing with an 11km climb.