Dallisgrass is a perennial that grows from roots each spring and grows seeds that germinate all summer. If you till the soil you will still have a problem because of the seeds in the soil. You can kill the existing weeds and surrounding lawn with a herbicide and then re-sod with weed free St Augustine. Read the label of the herbicide you select to see how long you have to wait before planting.
Dallisgrass is a coarse-textured grass that grows in a clump and slowly increases in diameter as its shallow, underground stems (short rhizomes) grow outward. The rhizomes have short internodes (the length of stem between the joints) that look like concentric rings on its surface. The leaf blades of dallisgrass are fairly wide (1⁄4 –1⁄2 inch) compared to desirable thinner turf grasses. If left unmowed, blades will grow 4 to 10 inches long. At the base of each leaf blade is a collar with a membranous ligule about ¼ inch long and no auricles or projections. At the base of the collar is the leaf sheath, which is slightly flattened. Frequently there is purplish coloration at the base of the grass stems (technically called culms). The flowering stalk (raceme) grows 14 to 65 inches tall and the flower head (inflorescence) consists of 2 to 10, often drooping, spikelets (delicate branches) that arise from different points at the top of the flower stalk. Each spikelet has two rows of flat, egg-shaped seeds along its entire length and is pale green to purplish in color. Dallisgrass produces abundant amounts of seed, which are its primary means of dispersal. Water, lawn mowers, and humans or pets spread the seed to new places. Seeds usually germinate in spring and summer when soil temperatures are in the 60° to 65°F range and grow to form new clumps. The optimum air temperature range for growth is 80° to 90°F and when temperatures are in this range, plants grow very rapidly. This weed is often found growing in wet areas such as drain ditches, low places, and in heavily irrigated turfgrass. It tolerates both sandy and heavy clay soils and, once established, is drought-resistant and frost-tolerant. A major component of dallisgrass management is preventing establishment of new plants. In home landscapes, removing young plants by digging them out before they form rhizomes or set seed is the best strategy for control. Mature plants can also be dug out, but they sometimes grow back if rhizomes are left behind. In professionally managed turfgrass areas, prevention is an important component in managing this weed. When dallisgrass is abundant or the plants are located over a large area, it may be necessary to supplement cultural practices with herbicides. Prevention Dallisgrass can be introduced into lawn areas with new turfgrass seed or sod, but often the seed is introduced on mowers that have been used in contaminated sites and then moved to weed-free sites. Cleaning a mower after mowing a contaminated site should reduce the chance of invasion into new areas. Inspect sod before taking delivery to make sure dallisgrass is not present. Don’t use soil from dallisgrass- contaminated areas to repair low or bare spots in lawns. In dallisgrass infested areas delay or minimize the amount of aeration performed on the turfgrass in spring when new seedlings germinate to avoid small open areas where dallisgrass plants might become established. Cultural Control Because dallisgrass is a perennial plant, persistence is required to kill it with cultural practices. In lawn areas the clumps can be removed by digging. Mowing the turfgrass will not remove dallisgrass, but when turfgrass is mowed at its optimum height, it is better able to resist an invasion of this weed. When dallisgrass has been established for some time in the turfgrass, seed will be abundantly present in the soil. In well-established turfgrass, seedlings may not be able to establish, but if there are open areas in the turf, seed will germinate in these areas. If bare areas are present, overseed them with desirable turfgrass species or sod to reestablish the turf. Dallisgrass is not normally a problem in ornamental beds, but if it does occur, the plants can be dug out and a thick layer of mulch laid over the area to control the seedlings. Along roadsides and fences or in orchards and vineyards, the plants can be dug out during summer and left in place for the clumps of rhizomes to dry. As long as all the rhizomes are dug up and dried, the plant will not regrow. New seed will continue to germinate and establish unless the seedlings are removed. Mulching with organic materials is not very effective for the control of mature dallisgrass. However, if the tops of the plants are removed down to the soil line, laying black plastic or landscape fabric over the area will control the remainder of the plant as well as any new seedlings. Summer solarization with clear plastic significantly helps control dallisgrass seed and reduces rhizome regrowth. Chemical Control Where digging out clumps of dallisgrass in turfgrass is not practical, herbicides may be used. Herbicides to control established plants are referred to as postemergent herbicides. These herbicides are either selective and kill only specific weeds, or they are nonselective and kill any plant they come in contact with. To control germinating seed, preemergent herbicides are used. In order to obtain complete control of this perennial grass weed, it is necessary to control both the established dallisgrass plant and the germinating seed. Established Plants in Turfgrass. Some turf managers and home gardeners use the nonselective herbicide glyphosate (Roundup) to control dallisgrass in turf. Glyphosate kills both the dallisgrass and the turfgrass, leaving an area of dead turf. To keep the turf vigorous and growing well enough to out compete germinating dallisgrass seed, the spot needs to be overseeded or a preemergent herbicide needs to be applied. Sometimes dallisgrass is not entirely killed after an herbicide treatment, even though the turf is severely damaged or killed, and retreatment may be required. Other nonselective postemergent herbicides are not as effective as glyphosate. Seed in Turfgrass. Preemergent herbicides can be used in established turfgrass to control germinating dallisgrass seed. Apply preemergent herbicides in late winter or early spring before dallisgrass seed germinates. Herbicides that control crabgrass such as benefin + oryzalin, bensulide, DCPA, dithiopyr, oryzalin, oxadiazon pendimethalin or prodiamine, are also effective on dallisgrass. (Bensulide, DCPA, and oxadiazon are for professional use only and may have some restrictions for use on residential lawns.) Preemergent herbicides used on lawns need to be irrigated into the soil with about ½ inch of water relatively soon after application in order to become effective. Consult the label for application details. Read and follow the directions carefully
Here is a fact sheet from University of California that suggests a combination of controls: