The 24-year-old Orica-GreenEDGE rider, already a stage winner last year, crossed ahead of world champion Michal Kwiatkowski (Etixx-QuickStep) and Katusha's Ilnur Zakarin.
On a rolling 162.7km course around Bilbao, Matthews came home at the front of a reduced group of around 50 riders after a three man break was captured before the finishing lap.
This result continued Matthews's fine start to the season having won a stage of Paris-Nice, where he also held the leader's yellow jersey, and finished third at Milan-San Remo.
"I was quite confident going into the stage," Matthews said. "We did a recon of the final climb yesterday and I knew what I was in for, it just came down to what legs I had today.
"It turned out I had really good legs, got myself over the climb and I knew from that reduced bunch I had a pretty good chance of cleaning up the sprint.
"There wasn't any lead out trains, it was more of a grovel, so I just placed myself within the top five in the final and started my sprint a little earlier, rather than waiting like I did in San Remo, so I couldn't get boxed in."
The favourites, including Giro d'Italia champion Nairo Quintana - who has already won Tirreno-Adriatico this year - finished safely in the lead bunch.
Quintana (Movistar) is expected to face competition for the overall victory from Kwiatkowski, who finished second behind Alberto Contador (Tinkoff-Saxo) last year.
The second stage takes the peloton over 175.4km from Bilbao to Vitoria with another hilly course, including a climb just 9km from the finish.
Stage 1 and general classification: 162.7km, Bilbao
1 Michael Matthews (AUS) Orica-GreenEDGE 3hr 57min 07sec
2 Michal Kwiatkowski (POL) Etixx-QuickStep
3 Ilnur Zakarin (RUS) Katusha
4 KÃ©vin Reza (FRA) FDJ.fr
5 Tony Gallopin (FRA) Lotto-Soudal
6 Julien Simon (FRA) Cofidis
7 Fabio Felline (ITA) Trek Factory Racing
8 Valerio Agnoli (ITA) Astana
9 Petr Vakoc (CZE) Etixx-QuickStep
10 Daniel Moreno (ESP) Katusha