Matthews was the clear winner on the tough uphill finishing straight at Stirling in the Adelaide Hills.
Tasmanian Matt Goss recovered from a puncture with about 10kms to go to finish among the leaders and regain the overall leadership.
Goss now has a two second lead over defending Tour champion, Andre Greipel of Germany.
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Matthews won the under 23 title last October at the world titles in Geelong and is in his first year as a senior professional.
He has had a strong start to the year, winning a race in the Bay Classic series and finishing third in the Australian Time Trial championship.
Australian Luke Durbridge, who won silver in the under 23 time trial at last year's world titles, was in a break of four riders who went clear in the 129km stage from suburban Unley.
But the main group never let them go too far ahead and they were caught just after the first of two finishing circuits at Stirling.
British sprint ace Mark Cavendish finished well down on the leaders as he tries to recover from the injuries he received in his nasty crash near the end of stage two.
Meanwhile, Australian cyclists Chris Sutton and Bernard Sulzberger were forced out of the Tour Down Under after Wednesday's crashes.
Sulzberger suffered a broken collarbone in the chaotic finish to stage two at Mannum, while Sutton badly cut his knee and suffered other abrasions in another accident a few kilometres earlier.
New race leader Robbie McEwen toned down his comments immediately after the stage, when he blamed gravel on the road for some of the carnage.
