The Australian capitalised on the work of team mate Nils Eekhoff who closed down a late attack with just under 2kms to go, Eekhoff smashing apart the bunch even further after taking a huge turn on the front.
Matthews then launched his sprint off the back of Mitchelton-Scott's Luka Mezgec on the final dig to the line leaving the Slovenian and Florian Sénéchal to round out the podium with Eekhoff too finishing strongly in sixth, raising his hands in the air behind Matthews.
Team Sunweb spent the day keeping a tight rein on the breakaway, whittling down the peloton and closing down attacks in the final 20kms.
“This is an amazing day,” a beaming Matthews said. “We’ve tried a lot of times to win this and today we came with a super strong team to try again.
"In the final Nils did a great job to start pulling and then he got a split with one other guy and I could sit on behind. Mezgec then closed the gap and I was able to do a really good sprint at the finish.
"It’s amazing to come here and win after so many tries and I just really want to thank the team for their amazing support today.”
"After Milano-Sanremo’s podium I was confident that I could finish it off if I got the opportunity today."
The WorldTour victory continues the Canberran's hot run of form, his performance at Milan-San Remo only hampered by a hand injury sustained in the closing kilometres and he still managed a third place.
Matthews will head to the Giro d'Italia in October instead of the Tour de France for the first time in five years.
It is the third time an Australian has won the race after Simon Gerrans in 2009 and Simon Goss in 2010.