The 27-year-old Scot's six-under 66 at 13th Beach Golf Links left him with an 18-under total of 270, one ahead of local duo Wade Ormsby and Brad Kennedy.
Law, who began the day three shots off overnight leader Ormsby, struck a brilliant approach to within 10 feet of the pin on the par-five 18th and coolly rolled in the eagle putt to pressure the leading Ormsby.
Ormsby, playing the hole behind, crumbled with a double-bogey on the par-three 17th to give Law the club-house lead when he dragged his tee-shot left and failed to make the green with a chip before missing the bogey putt from about 10 feet.
The Australian also missed a long eagle putt on the last that would have forced a playoff.
"We stood on the tee and we said we need to make eagle," Law said after claiming the A$1.5 million ($1.06 million/£819,000) winner's cheque.
"We had to go for it, so I sort of took a bit off a hybrid and lucky it went to eight-10 feet. At the time I was just trying to get into solo second.
"It's an amazing event, we've loved it all week."
Kennedy made a strong start, with six birdies before the turn, but had two bogeys on the back nine and had to settle for a share of second.
South African Justin Harding finished fourth, a stroke further back on 16-under.
In the women's tournament, France's Celine Boutier eased to a two-stroke victory after an even par final round that moved her to eight-under overall, ahead of Australian duo Sarah Kemp and Su Oh in joint second.
Kemp opened her round with a double bogey but struck nine birdies to finish strong, unlike overnight leader Kim Kaufman, who blew a two-stroke lead with a disappointing six-over 78 and finished in a tie for eighth place.
(Reporting by Simon Jennings in Bengaluru; Editing by Ian Ransom/Amlan Chakraborty)
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