Nowadays, the buzzwords for organizations to be prepared for the competitive environment’s challenges are sustainability, digitalization, resilience and agility. However, despite the fact that these concepts have come into common use at the level of both scholars and practitioners, the nature of the relation between sustainability and resilience has not yet been sufficiently clarified. Above all, there is still no evidence of what factors determine greater resilience to change in an organization that also wants to be more sustainable, especially in times of crisis and discontinuity. This research aims to explore from a theoretical point of view, through the construction of a conceptual model, how these dimensions interact to help the business to become strategically resilient by leveraging digitization and agility as enablers. A new view of resilience arises from the study, which goes beyond the well-known ability to absorb or adapt to adversity, to also include a strategic attribute that could help companies capture change-related opportunities to design new ways of doing business under stress. A key set of strategically agile processes, enabled by digitalization, creates strategic resilience that also includes a proactive, opportunity-focused attitude in the face of change. Strategic resilience to lead to organizational sustainability must be understood as a multi-domain concept quite similar to the holistic view of sustainability: environment, economy and society. Finally, the research offers a set of propositions and a theoretical framework that can be empirically validated.