The Orica-GreenEDGE rider now leads Evans (BMC) by 21 seconds on the general classification with Rigoberto Uran (Omega Pharma-QuickStep) third at one minute and 18 seconds.
"It was all for the win today," said Matthews. "Fair play. It was me against him (Cadel Evans) for the jersey and the stage, and I was lucky enough to have really good legs in the final after my team put me in the perfect condition at the bottom of the climb.
"On this sort of terrain, it's definitely my best win, and totally a dream come true. Winning a hilltop finish over Cadel Evans while wearing the Maglia Rosa in the Giro d'Italia: it doesn't get much better than that."
The two Australians were the biggest beneficiaries of of massive crash which decimated the majority of the peloton with just nine kilometres left in the race.
The crash split the peloton leaving all of Evans's general classification rivals stranded and with work to do for the remaining 15 stages.
Ten kilometres of extra distance was added to the stage after a landslide forced a detour, making it the longest stage of the race at 257km. The increased distance meant that it took over six hours for the peloton to get to the decisive 8.6km long climb in Monte Cassino.
Even though he had targeted the stage for a possible victory, Matthews was not expected to be with the best of the best on the 8.6km finishing climb with its average gradient of 5.1 per cent. But events and good legs played in his favour, giving him the biggest win of his career, and Evans a lead which puts him in the box seat to win his second Grand Tour.
"It was only when I saw our group was so small and the types of riders that were there that, that it wasn't because of the normal racing conditions that we had a selection like that unfortunately," said Evans.
"The communication in the final isn't clear and to make rational decisions for such an unexpected situation isn't easy. Our job is to race and to race to the finish. That's the first thing on our mind. What happened behind, I really have no idea. I haven't seen it. Unfortunately, it has been a very bad day for some of the riders."
Marco Bandiera (Androni Giocattoli), Edoardo Zardini (Bardiani-CSF), Andrea Fedi (Neri Sottoli) and Edwin Avila (Colombia) were the four escapees of the day, spending the majority of the stage from Sassano with a five minute buffer on a relaxed peloton.
The stage continued at a steady pace as the time gap inched down to 1min 45sec at 30km, until the break was finally caught with 11km left to go.
Two kilometres later a series of crashes on a roundabout split the peloton with the climb to Monte Cassino only metres away, with Katusha's Joaquim Rodriguez the biggest general classification casualty.
Evans and Matthews were among seven riders who stayed out of trouble with smart positioning, while behind, the remains of the peloton, which included Uran and Movistar's Nairo Quintana chased desperately.
Evans led as the finish line approached while Matthews, with his sprinters acceleration, waited patiently before making his move.
When the move did come Evans could not respond and Matthews cantered home to victory with Lotto-Belisol’s Tim Wellens in his wake.
The seventh stage is one for the sprinters with a 231km ride from Frosinone to Foligno.
"We'll try again for the win tomorrow," said Matthews. "We have a really strong team for the lead-outs, as we showed in the opening team time trial.
"We're not going to back down now: we have two stage wins now. We'll push all the way and see how far we can get."
Stage 6: 257km, Sassano to Monte Cassino
1 Michael Matthews (AUS) Orica-GreenEDGE 6hr 37min 1sec
2 Tim Wellens (BEL) Lotto-Belisol
3 Cadel Evans (AUS) BMC
4 Matteo Rabottini (ITA) Neri Sottoli-Yellow Fluo
5 Ivan Santaromita (ITA)Orica-GreenEDGE 0:00:13
6 Steve Morabito (SUI) BMC 0:00:23
7 Wilco Kelderman (NED) Belkin 0:00:49
8 Mauro Finetto (ITA) Neri Sottoli-Yellow Fluo
9 Diego Ulissi (ITA) Lampre-Merida
10 Fabio Duarte (COL) Colombia
1 Michael Matthews (AUS) Orica-GreenEDGE 24hr 18min 14sec
2 Cadel Evans (AUS) BMC 0:00:21
3 Rigoberto Uran (COL) Omega Pharma-QuickStep 0:01:18
4 Steve Morabito (SUI) BMC 0:01:25
5 Matteo Rabottini (ITA) Neri Sottoli-Yellow Fluo
6 Ivan Santaromita (ITA) Orica-GreenEDGE 0:01:47
7 Fabio Aru (ITA) Astana 0:01:51
8 Tim Wellens (BEL) Lotto-Belisol 0:01:52
9 Ivan Basso (ITA) Cannondale 0:02:06
10 Nairo Quintana (COL) Movistar 0:02:08
SBS will broadcast every stage of the 2014 Giro d'Italia LIVE! There will be nightly highlights at 5:30pm on SBS ONE, and each stage will also be streamed live here at Cycling Central.
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