Day pulled away from the chasing back after a run of three successive birdies on the back nine, but failed to hold his nerve at the crucial moment.
Successive bogeys at 16 and 17 pushed Day out of contention, leaving Cabreba and Scott to battle it out for the famous green jacket at the final hole.
Scott looked to have done enough after scoring a birdie at the 18th with a terrific putt from 25 feet to move clear at nine under, but Cabrera battled back again to set up his own birdie chance at the last with superb approach play.
Cabrera stayed calm to force a playoff with a short putt, leaving the Argentine and the Scott needing extra holes to decide who claims the title in Georgia.
Both players drove with authority at the 18th green to start the first playoff hole, before making the same mistake to pitch their approaches in an almost identical spot just short of the green.
Cabrera went close as his long putt whistled just past the hole, with Scott sending his effort five feet short. The Australian held firm to putt and send it to a second extra hole.
A sudden-death shootout continued at the 10th as both men found prime position at the green in two shots.
Cabrera sent a teasing putt just beyond the hole, giving Scott the chance to birdie from 12 feet and claim the green jacket.
The Aussie made no mistake with a precise putt to finally end his Masters hoodoo on a marathon final day.