Would pouring boiling water over periwinkle kill the plants?
Boiling water will probably kill the tops of the plants (leaves, maybe some stems). However, you probably can't carry enough boiling water out to the garden to get it to percolate down to the roots. Most likely, the periwinkle will come back.
If you go this route, please be careful. You can be more seriously hurt with boiling water than you can with a squirt bottle of Roundup.