Killing invasive ground cover is a much easier project when there are not other plants or grass in the area needing to be saved. Fortunately, you can take some steps to kill such plants, yet leave the surrounding areas mainly unscathed. It may take some extra time and preparation, but in the end it saves on having to replant an entire yard.
Kill as much of the undesired growth as you can using a post-emergent herbicide. Keep a buffer of at least 12 inches from other plants.
Cover weeds near plants that you desire to keep with sheets, plastic or newspaper. These sheets or plastic should be black or otherwise opaque so as not to let any light through.
Rake up the dead vegetation as soon as it dies. This helps to clean up the area for the new growth, which may be introduced immediately in some cases.
Use a pre-emergent herbicide to kill any remaining seeds from the plants.
Plant new plants in the fall after using a pre-emergent herbicide in the spring if using seed. If using established plants, you should not have to wait at all, though waiting a short period of time, such as a week, would not hurt, in case there are any adverse reactions to the herbicide present in the soil.