Anneveld took 4-21 from four overs as the Meteors restricted the home side to 9-101 in reply to 6-129.
The Meteors, who won the toss and elected to bat, made a strong start through openers Laura Wright (11 off 16 balls) and Asha Smith (22 off 15).
Captain Kris Britt added 29 from 25 deliveries, while Sara Hungerford (20 off 23) and Kate Owen (21 off 20) also proved valuable.
Anneveld (two off six) was the only batswoman to fall cheaply, with Rhiannon Dick (four off 11) and Sally Moylan (six off four) left unbeaten at the crease.
Alex Price (2-18) and Jakarra Hill (2-26) took two wickets each, while Tahlia McGrath (1-15) and skipper Lauren Ebsary (1-31) claimed one apiece.
Openers Alicia Dean (20 off 22) and Beth Morgan (18 off 12) ensured the Scorpions got their run chase underway on a positive note.
Ebsary chipped in with 25 from 23 balls before South Australia lost six wickets for just 22 runs.
Kylie Rattray (seven off 14), Rhianna Peate (nine off 16) and Bridget Patterson (one off five) failed to make an impact, with Megan Schutt (three off six), McGrath (five off nine) and Alex Price (zero) also falling cheaply.
Owen was economical for the Meteors with 3-11, while Sian Ruck (1-20) and Sally Moylan (1-25) also took wickets as Anneveld stood out.
