It might, but have you tried using several layers of wet newspaper and then mulch? It seems to work for my crab grass problems.

I think you would need to smother (as you describe) AND do a cut off trench around the area that you are trying to garden. The weed you describe has a rhizomatous root system, which means that even if you kill everything off in one area, there are still roots waiting to grow in the unkilled area, that will eventually creep back into the surrounding areas.

One way to prevent the creep of rhizomatous plants is to build a cut off trench or cut off wall that acts as a barrier for those roots.

Many will disagree with me, but if I were in your situation, I'd hit them with Roundup, till. After tilling, I'd wait again to see what comes up and hit it with Roundup again to make sure any seeds that might have been there are dead too.

Sometimes in life, you just have to bite the bullet!

I think joepyeweed has a major step in the process. A rhizome barrier or trench around your planting area is the first step. Then you might try the black plastic.

You could also try the smothering again but be sure to use a bottom layer that the grass can't pop up through. Thick paper or cardboard layered with no gaps and then covered over with the mulch.

Perhaps even a combination approach. Dig that trench then lay your paper/cardboard layers over the intended garden. Then make a nice set of lasagna layers with mulch materials and cover over the whole thing with the plastic and let it cook. Take special pains to make sure that the cardboard/paper and plastic cover the edges of your planting area well and are good and secure down in the trench.

With some luck you will have a wonderful rich stuff to plant in at least for a while before your weeds come back.

Since you are growing vegetables, my inclination would be to hand dig the garden in the spring with a spade or garden fork. This will allow you to pick out the rhizomes and roots as you turn the soil. This has worked for me in the past. Adding a trench around the perimeter will reduce rhizome penetration.

Do this every spring and you will have a weed free garden.

Black plastic may smother the weeds, but if you wait until summer, clear plastic could do an even more thorough job. The process is known as solarizing. You water the area you want to kill, then place the clear plastic over the top, weighing down the sides. The sun goes through and heats up the soil underneath, killing pretty much everything (including roots, rhizomes and microbes).

Devil grass could be either Bermuda or Quack Grass depending on where in the world you are. The only really effective method of eliminating either of them, however, is digging the rhizomes out and then putting a good, solid barrier between that cleaned out area and where it is growing. Putting black plastic down to kill the growth can cause the soil under that plastic to become anaerobic, airless, and the soil microbes that are needed to digest dead plant material in your soil and feed the plants growing there need air, aerobic bacteria. If I read the signature correctly I think you are in upper New York, zone 4, so you do not have enough of a growing season for "solarizing" to work, so that is not an option and won't work anyway. Weed, or grass poisons are not a good idea because they need to be used often to control that unwanted growth, in other words they do not kill all of the root and the plants grow back, eventually, and Cornell has found that many weeds on farms are resistant to these products today.
When you dig the rhizomes out you need to be sure you get as many as possible, and keep watch for new growth later and pull those out as quickly as possible. Sometimes, in planting beds I have had barriers around for a long time, I still find some quack grass growing and when I pull that out I will get a rhizome 3 to 6 feet long.

crapjoe has the only solution--I've tried EVERYTHING listed-they just dont work!! trench sounds good--as does all the rest-untill you understand that, as a expert tells me, the roots go FEET down--and it can travel by rhizomes, touching ground (tip rooting) or by SEEDS. So unless youre willing to kill off everything with in miles, chemical is the only way to go. and not just once--keep the sprayer handy. Best advice I ever got was to try to keep a border clear, and just fight what crosses. Other solutions sound best for the enviorment, I know, But I live with the stuff-and know-, fought it over 40 years. sometimes it just has to be-you eat--or it eats.

I have bermuda grass here that acts in the very same way, extremely hard to get rid of. I use a lot of mulch in my gardening, and have found the only way to get rid of it is Round Up, unfortunately. However, the good news is that once I give a patch of grass the old Round Up treatment and let it die off, I can cover it with mulch and plant. When the odd grass pokes its head out, the soil is so loose that I can pull it out roots and all. So I generally just use the single application of Round Up and deal with the odd grass sprout from there.

crab,
"if I were in your situation, I'd hit them with Roundup .. Sometimes in life, you just have to bite the bullet!"

NOOOoooooooooo! welll ... not yet, anyway.

btw - what exactly is roundup (besides a poison)?

kim,
"I think you are in upper New York, zone 4, so you do not have enough of a growing season for "solarizing" to work, so that is not an option and won't work anyway"

yup, fort ann, (near lake george). but i would disagree about the length of growing season as it has been getting longer and longer, almost each year.

If you really want to be rid of an aggressive grass you will have to think and act long term and probably use a very concerted and combined approach. A roto tiller will not help much and will quite possibly make the problem worse by creating several more independently growing fragments.
If you have a big enough area, renting a sod stripper would be justified, otherwise stipping sod with a flat shovel is in order. That won't be the end of the battle but a beginning. A trench barrier is definitely also in order. The contents of "Roundup" depend on which version you buy. The main ingredient is glyophosphate which is relatively benign (as far as we know yet anyway) but some formulations of "Roundup" now have other poisons so be sure which one you are getting. Glyophosphate is not selective so don't get it on anything you don't want to harm. Glyophosphate works by spraying on green portions of the plant and not very well on woody portions although it can be used effectively if painted onto a cut stump immediately after cutting (worked for me on Ailanthus trees). Glyophosphate does not work by spraying on soil. Some places sell pure glyophosphate concentrate without the other stuff in it (but sometimes some detergent as a surfactant).
I would probably strip the sod and make the protective trench, spray what comes back and then thoroughly mulch with black plastic for a few seasons. After that you will have to watch again for resprouting. If using herbicide makes you uncomfortable you can skip that step. If it is o.k. at that point then plant a cover crop or something to compete with and prevent reemergence. Many weed seeds last for years.

Here is a link that might be useful: Article about glyophosphate