Land use is known to reduce the diversity of species and complexity of biotic interactions. In theory, interaction networks can be used to predict the sensitivity of species against co-extinction, but this has rarely been applied to real ecosystems facing variable land-use impacts. We investigated plant-pollinator networks on 119 grasslands that varied quantitatively in management regime, yielding 25401 visits by 741 pollinator species on 166 plant species. Species-specific plant and pollinator responses to land use were significantly predicted by the weighted average land-use response of each species' partners. Moreover, more specialized pollinators were more vulnerable than generalists. Both predictions are based on the relative interaction strengths provided by the observed interaction network. Losses in flower and pollinator diversity were linked, and mutual dependence between plants and pollinators accelerates the observed parallel declines in response to land-use intensification. Our findings confirm that ecological networks help to predict natural community responses to disturbance and possible secondary extinctions.