Nassella neesiana (Chilean needle grass), an invasive ‘sleeper weed’ established in sheep and beef pastures in three of New Zealand’s sixteen local government regions, has a potential geographic range amounting to 3.96 million hectares spanning all regions except the West Coast. It impacts the productivity, market value and welfare of livestock through its sharp penetrating that cause blindness and the downgrading of wool, hides, and carcasses. In this study we estimate the benefit of preventing its spread as the present value (PV) of local (regional) and national productivity losses that would accrue over 200 years under a ‘do nothing’ spread scenario. Using a 3% discount rate and two assumed spread rates, 201 and 100 years to 90% occupation of its potential range, we calculate national PV losses of NZ$ 192 million and NZ$ 1,160 million respectively. In a breakeven analysis, these losses, which equate to the national benefits of preventing the spread, justify annual expenditures of NZ$ 5.3 million and NZ$ 34 million respectively. Restricting the analyses to the regions with known infestations (Hawke’s Bay, Marlborough, Canterbury) provided much lower estimates of the benefits (ranging from NZ$ 16.8 million to NZ$ 158 million) because spillover benefits from preventing spread to the other susceptible regions are not accounted for. These analyses support a nationally coordinated approach to managing N. neesiana in New Zealand involving surveillance and control measures respectively in the susceptible and infested regions.