Scott, 32, sunk a 15-foot putt on the 10th green on the second play-off hole to prevent 2009 winner Cabrera reclaiming the famous Green Jacket.
Both Scott and Cabrera finished on -9 after four days playing around Augusta’s famous course with Jason Day, a runner-up with Scott in 2011, finishing in third on -7.
Former champion Tiger Woods tied for fourth with another Australian Marc Leishman on five under.
Scott was delighted to become the first Aussie to claim the heralded Green Jacket, saying: "It fell my way today, there was some luck there but it's incredible to be in this position. I'm honoured."
"This is the one thing in golf we hadn't been able to achieve," he added. "It's amazing that it's my destiny to be the first Australian to win."
The Aussie squandered a four-shot lead with four holes remaining at the Open last year, allowing Ernie Els to swoop in and steal the title from under Scott’s nose.
However, he kept his nerve this time around to roll in a superb birdie putt on the final 18th to move one shot ahead of Cabrera who was waiting down the fairway in the final group.
The Argentine kept his focus despite the noise from the green and hit his approach just a few feet from the pin before sinking his birdie for a round of 70 to join Scott on nine under.
Both players were feeling the nerves and landed short of the green on the first of their two play-off holes. Cabrera played first and his ball nearly dropped into the hole from his chip shot, but landed short. He finished off his hole with four shots.
Scott left his chip three feet shy but sunk it and they both headed back down to the 10th. Both players hit the centre of the green with their approach shots but Cabrera missed his putt to allow Scott his chance to seal the victory.
"That's how golf is. I came back and I had that chip on 18, I could have won it," said Cabrera.
"But Adam's a good winner. I would have been happier if I had won but he's a great player, I get along with him, we've played together in the President's Cup and I'm happy for him."
England’s Lee Westwood once again led the charge for the English players but fell well short in the end, on -3.
Sergio Garcia also finished on three under while other Europeans Luke Donald, Justin Rose and World number 2, Rory McIlroy, finished on +2, ending a disappointing week for the Europeans.
However, McIlroy knows where he went wrong: “Yesterday [round of 79] was very disappointing. If I had kept that round under control then I might have been in with a chance today. But I was pleased with my round today and that is something to build on for the rest of the season.”
Chinese 14-year-old amateur Guan Tianlang finished with a 75 to card +12 on his debut that saw him become the youngest Masters competitor and - remarkably - the youngest player to ever make the cut at a major, and winner of the low amateur prize.
image: © Hone Morihana