South African work has shown that yellow nutgrass could be controlled to varying degrees by the allelopathic characteristics of ryegrass. This means that if you overseed turf with a high endophyte perennial ryegrass it will help counter this problem weed.
Sugar kills yellow nutgrass. The best time to do this is in spring as the nutgrass begins to sprout.
Simply sprinkle sugar over your entire lawn and give it a light watering to wash it into the soil. Then let it work its magic. The sugar eats away the nutgrass (but leaves everything else alone). It's best to do this process three or four times during spring to make sure you get any new growth or hardy plants that survived the first couple of hits. You can use granulated or powdered sugar sprinkled lightly over your lawn or a molasses spray. (Mix molasses at a rate of 450 mL to 40L of water in a backpack or manual sprayer.)
Mechanical removal. If you are going to do this you MUST remove the rhizomes and nutlets or it will regenerate.
Maintain a thick healthy cover of healthy grass and maintain this at a higher height of cut than usual. The shade will prevent the nutgrass from germinating.