Answer: Nutgrass (or nutsedge, its proper name) is indeed a pesky foe! You have a couple of options for controlling it. Although none of them are quick and easy, they will work if you are diligent.
The first option is to rototill and hand dig the nutlets. Each time you till the soil, pick out exposed roots with nutlets. Then wait a few weeks for more to sprout and till again.
A second option is to spray the nutsedge with a herbicide containing glyphosate (such as Roundup). Wait until the nutsedge is actively growing and has at least 3 to 5 leaves before spraying the patch, and apply the herbicide at the full labelled strength. This will knock it back severely. It will return and you should be ready to spray again. After several applications, you will find that the vast majority of the nutsedge is gone.
The key to any approach is to never allow it to reestablish and regain its stored reserves. Keep forcing it to use stored reserves to send up more growth and then quickly dig, rototill or spray it again. If you don't quit you will win!
Good luck with the war on nutsedge!
Q&A Library Searching Tips