The 28-year-old Australian started the final round seven shots off the lead.
But with 50 km/h winds - gusting at times to 70 km/h around the links layout on Sunday - there was a feeling that anything could happen.
Oh carded a closing two-over 74 , which ended up being the equal-low round of the day.
She then a had a nervous two-hour wait before finally being declared the winner when Shina Kanazawa's long birdie attempt at the 18th slid by the hole.
"I knew when it was windy I probably had more chance than if there was no wind," said Oh.
"I knew if I just played decent I was going to get close but I didn't think I would actually win.
"I think it's the toughest conditions I've every played in and putting was the trickiest."
Overnight leader Madoka Kimura (83), fellow Japanese player Kanazawa (80) and Australian Kelsey Bennett (81) struggled all day in the final group.
Oh finished at level-par 289, a shot ahead of Kanazawa, with Kimura one stroke further back in outright third.
Defending champion Ashley Lau from Malaysia and Australians Bennett, Robyn Choi and Kathryn Norris tied for fourth at three over.
Oh famously first qualified for the Australian Open as a 12-year-old back in 2009.
She and Minjee Lee combined to win a World Amateur title in 2014 and it seemed certain both were destined for great things.
But while Lee very much delivered on that potential after turning professional, Oh often struggled.
Her only two previous wins as a pro were also in Australia - at the 2015 Ladies Masters and the 2022 WPGA Championship.
She has also been a regular contender at the Vic Open, with five other top-10s including a runners-up effort in 2015.
Oh lost her LPGA Tour card in 2022 and then spent much of the previous two years on the US secondary tour.
Things started to turn around last year when she linked up with celebrated coach Ritchie Smith, whose stable also includes Minjee and Min Woo Lee, Hannah Green and Elvis Smylie.
She led after the first round of the 2024 Australian Open before finishing 14th.
Sunday's victory is another huge confidence boost.
"I love this tournament and hopefully we'll be back here next year," said Oh.
"I've always been quite close here and everyone who has won here is pretty good so hopefully I'll follow in that trajectory and have a good year."
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