The Australian also retained the maglia rosa as he faced reduced competition from his rival sprinters, after many of them fell away from the peloton on the category two climb, Barbagelata, which the riders crested 50km from the finish.
It was then a fast and flat run into town after a narrow descent from the climb, which caught out Domenico Pozzovivo, who took a nasty fall which saw him abandon the race after being carried away in an ambulance.
But as the main bunch ran into town, the result almost looked inevitable, with Orica-GreenEdge driving the pace on the front through Peter Weening and later Simon Gerrans, before Matthews launched his sprint to take victory by half-a-bike length.
Matthews's Orica teammates had been the main instigators in chasing down the day's breakaway, which had hovered at arms-length from the peloton for most of the short 136km stage.
The break had begun as a 25-man strong group, with the likes of Tom Boonen (Etixx - Quick-Step), Philippe Gilbert (BMC) and Matthews's teammate Simon Clarke all making the jump to the group at the stage's start.
The time (which only stretched to around three minutes) and the group's numbers began to fall away as they approched the climb, with Pavel Kochetkov (Katusha) making the most significant attack towards the top of Barbagelata, earning himself the blue mountains jersey.
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The Russian went solo for much of the descent, before being joined by the likes of Adam Hansen (Lotto-Soudal), Maciej Paterski (CCC) as well as Simon Clarke, who bridged the gap from the chasing group.
Clarke refused to work with his leading companions, while his teammates continued to drive on the front of the peloton to bring the foursome back, which they inevitably did with 3km remaining.
It was then down to the sprint, with Matthews finishing victorious and sealing another day in the pink leader's jersey.
Tuesday's stage four sees the riders take on another tricky hilly profile, with a category three climb 10km from the finish throwing a spanner in the works for any sprinters looking for another chance at a stage win.
