Wait until the early spring, after the last frost of the season, but before the periwinkles begin to grow again.
Mow, trim or cut back periwinkle down to about 4 inches every two to three years at this time. This will help keep it contained and from spreading.
Install a garden edge into the soil where you don't want the periwinkle to spread. Plastic lawn edging that is inserted several inches into the soil works well.
Remove periwinkle growing outside of its bounds manually by digging or pulling it out. You can also use a garden rake or hoe to remove it. Remove it again if it grows back.