Norris started a shot behind overnight leader Wade Ormsby but surged four clear of the field with six birdies and a single bogey before the turn.
Bogeys at the 10 and 15th were mitigated by a seventh birdie at the 13th and he parred the final three holes to finish with a comfortable cushion over compatriots James Marchesani and David McKenzie as well as Thai Jazz Janewattananond.
"It's taken me 21 years to have a win like this," Norris said after receiving the trophy from Fiji President George Konrote.
"Now I've got a start in Europe and Asia as well. I was going to quit the game last year and now I'm playing all over the world. It's just fantastic."
Jazz Janewattananond stormed up the leaderboard with a flawless 64, the 21-year-old hitting six birdies and an eagle three at the par five 17 to claim a share of second with Marchesani (70) and McKenzie (67).
Canada's Mike Weir finished with a 74 for a share of 35th, a shot better off than his fellow former U.S. Masters champions Angel Cabrera (74) and local Vijay Singh (71) who were among the players tied for 41st on one-under.
(Reporting by Nick Mulvenney in Sydney; Editing by Greg Stutchbury)
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