Scott's putt to capture the 77th edition of one of golf's premier events was set up when Cabrera's earlier try for an 18-foot birdie on the 10th hole at Augusta National came up 2 inches short.
The Australian responded by pouring his try straight into the hole.
The second extra hole was necessitated when each golfer netted a par on the first playoff hole, held on the 18th.
Scott positioned himself to win in regulation when he birdied the final hole to finish with a 3-under-par 69, moving a shot ahead of Cabrera.
But the Argentine forced a playoff by following with a birdie of his own, carding a 2-under 70 to join Scott at 9-under 279.
Two other Australians finished in the Top 4 -- Jason Day took third place at minus-7 after carding a 2-under 70 while Marc Leishman shared fourth with a 72 in the final round to finish at 5-under 283.
Four-time champion Tiger Woods also ended with a share of fourth after registering a 2-under 70.
Earlier Sunday, 14-year-old amateur Tian-lang Guan of China completed a historic Masters appearance, carding a final-round 3-over 75 to end at 12-over-par 300.
The teen became the youngest player ever to start the Masters and the youngest player to make the cut at the event.
His appearance, however, was overshadowed by a controversy over a 1-stroke penalty assessed for slow in Friday's second round. The decision was criticized by many, including Guan's playing partner, two-time Masters champion Ben Crenshaw.