It was sweet redemption for Scott who had surrendered a four-shot lead with four holes to play in last year's British Open, where he was runner-up to Ernie Els.
"I don't know how that happens," said Scott after his win.
"It seems a long way away from a couple of years ago here and even last July when I was trying to win another major.
"It fell my way today. There was some luck there somewhere. I don't know how to digest it at all at the moment but it was incredible.
"It's incredible to be in this position. I'm honoured."
Earlier Scott holed a seven-metre birdie putt on the last hole of regulation play to shoot a closing three-under-par 69 and finish at nine-under-279.
But 43-year-old Cabrera nailed his approach shot at the 18th, putting it within a metre of the hole and matched Scott's birdie to tie him with a round of 70.
Scott's countryman Jason Day finished outright third, two shots back after a closing 70.
Day had stood on the 16th tee with a two shot lead but leaked home with two bogeys.
Scott and Cabrera returned to the 18th for the first play-off hole.
After piping drives down the middle Scott fired into the green first and was short, sucking the ball back off the green.
But Cabrera couldn't respond, producing an almost identical shot.
Cabrera then went close to holing the chip shot, but both made par to send the playoff to the 10th.
Scott once again sent his drive down the middle and Cabrera used iron to match him.
Both men hit the putting surface; Cabrera had five metres feet, while Scott was left to negotiate four metres.
Cabrera's putt settled on the edge giving Scott the stage and flung his arms in the air as a flkood of pent up emotion poured out when his putt rolled in.
Fellow Australian Marc Leishman (72) finished off a fantastic week to end at five-under, tied for fourth with Tiger Woods (70).
Scott, who bogeyed his nemesis first hole but birdied the third with a lovely curling putt then made nine straight pars before nailing a birdie on the 13th thanks to some luck with Rae's Creek.
Scott's approach was sucking back towards the water but managed to stay up on the bank.
He then chipped to close, made the birdie and was back in the mix.
He faced a makeable eagle try on the 15th but managed only birdie. Still it was good enough to share the lead as Day bogeyed ahead.
While Day stumbled Cabrera continued the challenge with a birdie on the 16th to join the lead.
The Argentinean barely missed another birdie on 17 before his 18th hole heroics.
THE BEST FINISHES BY AUSTRALIAN GOLFERS AT THE MASTERS
Winner:-
2013 - Adam Scott
Outright second
1950 - Jim Ferrier
1996 - Greg Norman
Tied for second
1972 - Bruce Crampton
1980 - Jack Newtown
1986 - Greg Norman
1987 - Greg Norman
2011 - Jason Day
2011 - Adam Scott
- AAP