I hard plastic edging might be the best answer for you. But before you go that route, does covering the grass with cardboard and then a couple inches of soil not kill it? It works for me, but then again I have fescue.

Tilling sounds like it would just chop it into small pieces that would then sprout from each little piece!

I have zoysia and use a sharp shovel to clean up the edges; it usually takes about a day and I throw all the trimmings into a yard waste bag. That keeps it at bay for the rest of the year.

First you get a backhoe and get rid of the soil/grass..then you get a dumptruck of good garden soil mixed with some bark fines, then you go to the big box store and buy edging.
And..resolve never to let your lawn turf go to seed.
Or, you move..that's what I did.

Seriously, centipede,zoysia and bermuda (especially wild) I consider soil contaminents you'll never control so they have to be discarded with the soil and a solid edging, deeply installed to prevent the runners from escaping into your flower bed.
One darn seed in your flower bed and the battle starts all over again.

I don't think centipede is that hard to keep at bay because it just has the above the ground runners. I have common Bermuda and it's truly horrible...maybe that's why I think Centipede isn't so bad. :) I agree with computergardener. I have used that method in another yard and it works fine. Althought it *will* take some upkeep, just make a trench a few inches deep around the bed and you'll be able to see it before it skips the trench.
Pam

Lasagna composting with newspaper and grass cuttings. Google it. It really works, to kill grass/weeds, as well as great soil-improver. I don't know why it works, but I know it does. Some folks believe tilling just destroys whatever structure you already have in your soil, so no-till is trendy. I layer newspaper (maybe 3-5 sheets, overlapping edges), then an inch or two of grass clippings, then newspaper again and so on. A few layers works great (more if you need more to smother grass), and a little mulch on top makes it all look pretty while the grass underneath is dying. Then in a couple of months, plant right in it.