The 22-year-old Orica-GreenEdge rider, a former under-23 world champion, outsprinted Argentina's Maximiliano Richeze and Belgian Gianni Meersman in a dash for the line at Lago de Sanabria.
Italian Vincenzo Nibali, the favourite for outright victory in Madrid on September 15, maintained his slender three second lead over Chris Horner of the United States in the overall standings.
"Twenty other riders could have won today, but my team delivered me to the right position and I had the legs to finish it off," Matthews told reporters.
"I wasn't expecting to get a win here before we started, but I knew I might be able to do it because my form is good. It's my biggest win for sure.
"I could feel the pressure to get a result here but when you're going well, that pressure's not a bad thing. It's only when you're in poor shape that you suffer."
Nicknamed ‘Bling' after he attended a track race in Australia as a teenager wearing a load of gold jewellery and cut-off jeans, Matthews gave special thanks to his sports director, Julian Dean.
"With about 20 kilometres to go, Julian radioed through a heck of a lot of information to us about the bunch sprint finish here, what the last few corners were like and where the difficult parts were," Matthews said.
"Without him telling us all that, I'd have been riding blind and I don't think I would have got the win."
Nibali said he was relieved that after four days of racing in Galicia on technical, narrow roads, the peloton was heading south into more straightforward terrain.
"It's been a very tough opening section of the Vuelta, but I've come through it in good shape and that's what counts," Nibali said. "I just hope tomorrow, which should be easier, we'll get through equally well."
(Editing by John Mehaffey)
