Firms can achieve trinomial sustainability goals if they can constantly build and rejuvenate their capabilities to adapt to new situations. However, few studies consider the interrelationships between the distinct capabilities pertinent to sustainable development and the impact of these capabilities on firm performance under diverse contexts, especially in emerging economies. Drawing on dynamic capability theory, we developed a model to test the links between dynamic sustainability capability, theorized as a higher order capability, and relational and managerial capabilities, theorized as lower order capabilities, to the firm's sustainability performance. Data collected from 210 large Indian manufacturing firms is analyzed using PLS‐SEM. Results confirm that dynamic sustainability capability has facilitating effects on environmental and social performance directly and indirectly through managerial capability. Although relational capability partially mediates the link between dynamic sustainability capability and social performance, it does not impact environmental performance. Further, the aforementioned relationships are affected by forces in the firms' environment. Most of the direct and indirect relationships are negatively moderated by organizational inertia and positively moderated by environmental turbulence. By investigating the hierarchically structured capabilities, this study guides firms to make strategic choices regarding resource calibration for sustainability. The study recommends that organizations looking to integrate dynamic sustainability capability as part of their strategic management should look at the sequential combinations of existing resources to achieve different sustainability targets. The study's findings also urge policymakers to consider environmental conditions while developing sustainability reforms.