The 32-year-old Queenslander showed nerves of steel as he holed the winning putt from four metres on Augusta's 10th hole after Cabrera left his birdie putt almost on the lip.
"It fell my way today, there was some luck there but it's incredible to be in this position. I'm honoured," said Scott, who squandered a four-shot lead with four to play to lose the Open to South Africa's Ernie Els last year.
He became the 10th Australian to win a men's major, the first since Geoff Ogilvy in the 2006 US Open.
"The thing I did well out there was just stay right where I was, wherever it was on the golf course. I stayed in that one shot," Scott said.
"Australia is a proud sporting nation and this was one notch on the belt that we've never got."
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