Matthews was too fast for Fabio Felline (Trek Factory Racing) and Philippe Gilbert (BMC) at the stage finish in Sestri Levante.
His success secured him another day in the Maglia Rosa to make it three in a row for Orica-GreenEDGE after Simon Gerrans donned the first leader's jersey when the team won the opening team time trial, and before he passed it to Matthews on Stage 2.
"It's been a dream come true so far for this Giro d'Italia. We planned for the team's time trial win and this was another big goal for us. We reconed it last week so we knew what was coming and what to expect. From then on it was try to do as best as we could and we pulled it off." - Michael Matthews.
It was an aggressive start to the short 136km stage from Rapallo with 25 riders getting clear of the peloton five kilometres in.
The group included Orica-GreenEDGE’s Esteban Chaves and Simon Clarke, birthday boy Adam Hansen (Lotto-Soudal), Tom Boonen (Etixx-QuickStep), Rubén Fernandez (Movistar), Diego Ulissi (Lampre-Merida) and a trio from BMC; Philippe Gilbert, Marcus Burghardt and Silvan Dillier.
With such a large group at the front of the race the peloton was careful to never allow them more than a two minute advantage over the rolling terrain. With two riders in the break Orica-GreenEDGE could shrug off the responsibility of leading the chase, which left Tinkoff-Saxo to repeat their efforts of the previous day on the front of the peloton.
As the bumpy terrain started to really grip, many of the sprinters struggled to keep pace and Andre Greipel (Lotto-Soudal) was one of the first big names dropped with more than 60km to go. The big German wasn’t alone however with many riders being shed off the back of the peloton over the following kilometres including Stage 2 winner Elia Viviani (Sky).
With 50km to go the breakaway, which itself had fractured into a number of smaller groups, was less than a minute in front of the peloton.
Katusha’s Pavel Kochetkov launched an attack just shy from the summit of the Barbagelata, the final climb of the stage, and rode away solo to claim the King of the Mountains points. He worked hard to extend his lead, forging a 25 second lead over the chasing group which included Clarke, Hansen and Gilbert.
Further back in the race AG2R’s Domenico Pozzovivo was involved in a nasty crash which saw him lie motionless on the road for some time before being transported by ambulance to hospital. Fortunately, his injuries are not as bad as first thought. He's current in a stable condition in San Martino hospital.
Above video: Michael Matthews talks to the media after winning Stage 3 and continuing his run in pink.
After climbing for most of the stage it was a fast run to the finish with the final 40km either downhill or flat. With 20km to go Kochetkov held a 30 second lead over the nine chasers with the peloton a minute behind.
A stalemate in the chase group prompted Hansen to attack, with Clarke quick to chase his wheel with Maciej Paterski (CCC Sprandi Polkowice) following. Clarke sat on, leaving Hansen to do the grunt work chasing Kochetkov, with the trio eventually catching the Russian 10.5km from the finish.
While the quartet committed to the task the peloton caught them with 3.3km to go.
Clarke left little in the tank as he immediately joined the front of the peloton to control for Matthews, setting a blinding pace as they thundered towards the finish. Gerrans took up the baton in the finishing straight, while Matthews held Felline’s wheel, timing his effort to perfection to pass the Italian to claim the stage honours.
Matthews holds a six second lead over team-mate Simon Clarke. Alberto Contador remains as the closest threat to the Maglia Rosa, 17 seconds down, while Richie Porte is still 20 seconds behind Contador.
Stage 3: 136km, Rapallo - Sestri Levante
1 Michael Matthews (AUS) Orica-GreenEDGE 3hr 33min 53sec
2 Fabio Felline (ITA) Trek Factory Racing
3 Philippe Gilbert (BEL) BMC Racing
4 Sergey Lagutin (RUS) Katusha
5 Paolo Tiralongo (ITA) Astana
6 Luca Paolini (ITA) Katusha
7 Francesco Gavazzi (ITA) Southeast
8 Enrico Battaglin (ITA() Bardiani-CSF
9 Luis Leon Sanchez (ESP) Astana
10 Yonathan Monsalve (VEN) Southeast
1 Michael Matthews (AUS) Orica-GreenEDGE 8hr 6min 27sec
2 Simon Clarke (AUS) Orica-GreenEDGE 0:00:06
3 Simon Gerrans (AUS) Orica-GreenEDGE 0:00:10
4 Esteban Chaves (COL) Orica-GreenEDGE
5 Roman Kreuziger (CZE) Tinkoff-Saxo 0:00:17
6 Alberto Contador (ESP) Tinkoff-Saxo
7 Michael Rogers (AUS) Tinkoff-Saxo
8 Paolo Tiralongo (ITA) Astana 0:00:23
9 Fabio Aru (ITA) Astana
10 Diego Rosa (ITA) Astana