Scott shot a 6-under 66 to finish at 17 under, three strokes ahead of Appleby and third-round leader Bubba Watson.
Playing together, Scott led Appleby by one stroke as they stood on the 18th tee, but Scott pulled his tee shot into the pond that lines the left side of the 488-yard hole, the course's most difficult.
Appleby drove into the fairway bunker, then immediately gave Scott a reprieve by hitting his approach into the water near the green.
Scott took his drop, hit his approach safely away from the water, then holed the par-saving putt. He pumped his fist, Tiger Woods-style, after the ball disappeared, and the crowd roared.
Appleby had a double bogey to finish with a 69. Watson birdied the last hole for a 72.
Scott became the sixth Australian to win the event, joining Appleby, Bruce Devlin, Bruce Crampton, David Graham and Robert Allenby. Appleby and Crampton have won it twice and the eight victories by Australians are the most in any U.S. tour event. Only the British Open (9) has had more champions from Down Under.
Appleby and Scott started the day three shots behind Watson, but caught him with birdies on three of their first five holes. The Aussies matched each other shot for shot from there until Appleby bogeyed the par-3 14th and lost the lead for good.
Players were allowed to lift, clean and place their balls in the fairway for the second straight day after a morning thunderstorm dumped a half-inch of rain.
PALM COAST, Fla. - Keith Fergus survived several late stumbles and held on to win the Ginn Championship to become the second man to win on the PGA, Champions and Nationwide tours.
Fergus shot a 70 to win the Champions Tour event by a shot over Mark O'Meara and Hale Irwin despite bogeying two of the last three holes at the Ocean Club at Hammock Beach.
Fergus secured the victory by making a 7-foot par putt at the par-3 17th hole. He then two- putted from 13 feet for bogey at the par-4 18th to finish at 12-under 204. O'Meara (69) and Irwin (68) tied at 11 under.
The victory for Fergus was his first as a professional since the 1994 Nationwide Tour's Boise Open. He won three times on the PGA Tour between 1981 and 1983.
Fergus became eligible for the Champions Tour in 2004 but had not won in 71 starts until Sunday. He earned $375,000 and became the eighth winner in eight events this season on the Champions Tour.