Dynamic capabilities and sustainability practices have become the center of attention for companies globally, but there is still a debate on how organizations can successfully develop dynamic capabilities and achieve sustainability for competitive advantage. This paper discusses the outcomes of a comprehensive systematic literature review (SLR) following the PRISMA guidelines and employs dynamic capabilities theory to suggest that strategic routines and competencies, integrated value chains, sustainability-oriented transformations, and strategic organizational developments are the drivers to effectively develop dynamic capabilities. Similarly, environmental-oriented sustainability, sustainable strategic management, sustainable dynamic capabilities, stakeholder-centric approach, sustainable supply chain management, operational excellence, sustainable research and development (R&D), and sustainability-oriented global business strategy are found to be the drivers to achieve overall corporate sustainability. Based on the findings, a conceptual model is proposed to obtain sustained competitive advantage by developing sustainable dynamic capabilities and achieving corporate sustainability.