This study examines how national institutional contexts influence the sustainable performance of higher education institutions (HEIs) in global sustainability rankings, primarily focusing on the Times Higher Education (THE) Impact Rankings. Grounded in the Varieties of Capitalism framework, it examines the interplay of institutional dimensions such as labor relations, intercompany relations, finance, education, and governance dynamics in driving HEIs’ contributions to the United Nations Sustainable Development Goals (SDGs). The study uses panel data analysis and the Generalized Method of Moments (GMM) to evaluate data from over 5,000 HEIs across 106 countries (2019–2024). Results reveal that institutional dynamics are pivotal for enhancing HEIs’ sustainable performance. This research underscores HEIs' dual role in addressing societal Grand Challenges by linking global sustainability benchmarks to local institutional realities. This study highlights the critical role of HEIs and offers actionable insights into understanding what defines a "good university” through sustainability-focused, context-sensitive strategies. It calls for a reimagined paradigm where HEIs are not only academic leaders but also transformative agents in global sustainability efforts.