Greig finished with a four-over-par 77, finishing each of the nines two over par and with a solitary birdie 3 on the blind driving 10th hole.
She is on track to represent Otago in the Toro Interprovincial tournament to be played at Sherwood Park, in Northland, in December.
Abigael Crawford (St Clair) came in second with 83 and Sharon Fitzgerald (Taieri Lakes) was a further shot back in third place.
The Otago selectors will now name the team to play Southland for the Salisbury Cup, which will be played in Invercargill on October 8.
The final trial will be the Otago matchplay at Balmacewen during Labour Weekend.
The South Island women’s interprovincial is also at Balmacewen during the following weekend.