Ko finished with a 72-hole total of 9-under 283 on the composite course at Royal Melbourne. Yang shot a final-round 72.
Ariya Jutanugarn of Thailand, who was tied with Ko after three rounds in the LPGA, European Tour and Australian Ladies event, shot a 76 to finish third, five strokes behind Ko.
It is Ko's ninth professional win and the first of 2015 after three victories last year.
Defending champion Karrie Webb, who won her fifth Australian Open last year at nearby Victoria Golf Club, shot 71 and finished 10 strokes behind.
Play was suspended for about an hour due to nearby thunderstorms and the threat of lightning.