Your best line of defense, I believe, is a healthy lawn. Apply a fertilizer this fall that will encourage good root growth and a strong start next spring. Healthy turf grass will help choke out spurge. However, if you take the herbicide route, ask your nurseryman for a post-emergent product that can be used without harming your lawn. St. Augustine is sensitive to some herbicides.
Gallery is a pre-emergent herbicide that can be used before germination early next spring.
You'll likely need to make more than one application. My sister gave me a Texas Star hibiscus three summers ago. It grows taller each year, and this summer it produced blooms. After the blooms fall off, a round growth appears where the bloom had been. It eventually turns brown and dries up, and at that time I remove it from the plant.