The leg-spinner compiled her highest score with the bat for 2019-20 with a match-winning 60 not out from 54 balls.
Earlier, 20-year-old pace bowler Ellie Falconer took her best Women's National Cricket League figures with 4/36 from eight overs to help dismiss Victoria for 191.
Stand-in captain Tahlia McGrath won the toss at Allan Border Field and elected to field, with Darcie Brown (1/35) getting the early breakthrough, removing Elyse Villani (14) in the fifth over.
Falconer went on to take the next four wickets, clearly troubling the Victorian batters.
Amy Vine (56) was eventually trapped lbw by Wellington (1/25) in the 44th over, after she had managed to hold on since Villani's dismissal.
McGrath (2/31) and Sam Betts (2/32) both took two, while Betts claimed the final wicket on the last delivery of Victoria's innings.
Chasing 192, South Australia was off to a shaky start, losing star batter Bridget Patterson (5) in the opening over, for her lowest score this season.
By the end of the seventh over, the Scorpions were in trouble at 3/18 after McGrath (11) and Eliza Doddridge (1) were both out cheaply.
Tegan McPharlin (47) and Emma de Broughe (38) then worked patiently at the crease, skillfully steadying the innings and combining for a 71-run stand.
The side still needed 101 runs to win when Wellington entered, however the 22-year-old managed to form a series of meaningful partnerships to finish the job with one over to spare.
The Scorpions remain in Brisbane to take on Queensland on Thursday from 10:30am ACDT for their last clash of the season.
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