Local favourite Jason Scrivener tied the 33-year-old South African for the lead briefly but Oosthuizen regained his sole possession of top spot after consecutive birdies on the seventh and eighth.
Oosthuizen's final round one-under-par 71 for a four-day total of 16-under 272 was eventually enough to keep him ahead of Frenchman Alexander Levy, while Scrivener finished a stroke further adrift in third.
The world number 21 admitted he was nervous after his false start but regained control to end a two-year title drought at the A$1.75 million ($1.25 million) event, which is also sanctioned by the Asian and Australian tours.
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"I missed the second and third greens and was a sort of little rattled after that," Oosthuizen told reporters after his win. "But I settled in nicely and got back to hitting greens and giving myself opportunities.
"Then I had a good stretch from holes seven through to 12, although I did leave myself with a vicious first putt on the last (from 50 feet) but luckily I had three so could afford the bogey."
Levy's birdie on the 18th meant Oosthuizen had a two-shot advantage heading into the final hole and his bogey was still good enough to see him home.
"The greens firmed out a little today so you needed to look at your speeds carefully and the lines changed quite a bit," said Oosthuizen, adding that he stayed up late to watch the Stormers defeat Bulls in their opening Super Rugby fixture but fell asleep when they were winning with five minutes to go.
"So it was slightly different but still good."
(Reporting by Sudipto Ganguly in Mumbai; Editing by John O'Brien)
