Looks to me like ground ivy. A broad leaf herbicide LABELED for zoysia should take care of. Make sure to read the label for any transitional warnings.

This looks like Hydrocotyle. See this previous post to Walter http://www.walterreeves.com/name-that-plant/close-but-not-ground-ivy/ In further efforts to identify this weed I’ve found an excellent shot from New Zealand http://ketenewplymouth.peoplesnetworknz.info/image_files/0000/0002/0359/Hydrocotyle_heteromeria__Hydrocotyle.JPG The weed is identified there as Hydrocotyle heteromeria and a synonym for that is Hydrocotyle Americana. Zoysia doesn’t like wet feet. Hydrocotyles love it. Avoid soggy soils in managing this weed. Refer to this link for some control options for Hydrocotyles http://www.turffiles.ncsu.edu/weeds/Pennywort.aspx