Zoysia grass is a warm-season turf grass. It grows rapidly, and thickly, and can stand a fair amount of abuse. Unfortunately, the qualities that make zoysia a desirable lawn grass also make it a frustrating garden pest. Zoysia grass often outgrows the confines of the lawn. And no matter how many times you edge, pull, dig or spray, it keeps coming back. The only way to keep zoysia grass out of your flower bed for good is to create an impenetrable barrier around it.
Remove all of the zoysia grass currently invading your garden. If the grass does not interfere with any of your plants' roots, dig it up (roots and all) with a spade. If removing the grass may harm your plants, use a small paintbrush to paint a glyphosate herbicide on the individual blades. Spraying the grass may kill your plants.
Edge your lawn. Use a lawn edger to create a clear, even border between the garden and the lawn.
Install black plastic lawn edging along the lawn/garden border. Use edging that is at least 5 inches deep. Use a sharp kitchen knife or other tool to cut a trench that is just as wide as the edging, roughly 6 inches deep and at a 90-degree angle to the ground. Then, push the edging into the ground so the top of the edging is flush with the soil line. Cover the top of the edging with a layer of garden soil to help hold it down.
Spread a 1-inch layer of organic mulch over the flowerbed. This will keep any dormant zoysia grass seeds or stolons from germinating.