The security, resilience, and sustainability of urban water supply systems (UWSS) are challenged by global change pressures, including climate and land use changes, rapid urbanization, and population growth. Building on prior work on UWSS security and resilience, we quantify the sustainability of UWSS based on the performance of local sustainable governance and the size of global water and ecological footprints. We develop a new framework that integrates security, resilience, and sustainability to investigate trade-offs between these three distinct and inter-related dimensions. Security refers to the level of services, resilience is the system's ability to respond to and recover from shocks, and sustainability refers to local and global impacts, and to the long-term viability of system services. Security and resilience are both relevant at local scale (city and surroundings), while for sustainability cross-scale and -sectoral feedbacks are important. We apply the new framework to seven cities selected from diverse hydro-climatic and socio-economic settings on four continents. We find that UWSS security, resilience, and local sustainability coevolve, while global sustainability correlates negatively with security. Approaching these interdependent goals requires governance strategies that balance the three dimensions within desirable and viable operating spaces. Cities outside these boundaries risk system failure in the short-term, due to lack of security and resilience, or face long-term consequences of unsustainable governance strategies. We discuss these risks in the context of poverty and rigidity traps. Our findings have strong implications for policy-making, strategic management, and for designing systems to operate sustainably at local and global scales.