Quality educational institutions are strategic tools for accelerating the attainment of Sustainable Development Goals (SDGs). All the 17 SDGs are interlinked. For instance, quality education (SDG4) reduces poverty (SDG 1,2) and inequalities (SDG10) and stimulates good health and wellbeing (SDG3). The paper applied unorthodox theoretical postulations such as convergence models, intergovernmentalism, neofunctionalism and neorealism in explaining how functional (educational) institutions are a necessary enabling environment in accelerating the attainment of SDGs. Empirically, the paper identified unclear modus operandi, lack of political will, political instability, small and fragmented markets and economies with heterogeneous characteristics, and lack of standardization of product and procedures, among other factors, as constraints to sustainability in tertiary education. A Vector Autoregressive (VAR) model was employed using data from 51 Sub-Saharan countries. The three variables were gross domestic product per capita (GDPP), governance and tertiary education expenditure. Results indicated significant short-run unidirectional causality from gross domestic product per capita and tertiary education expenditure to governance, but joint short-run causality was not established. However, transmission effects across the three variables became significant as the number of years increased to ten years. The study recommends a holistic approach from policymakers in order to ensure sustainability in tertiary education due to interlinkages, with emphasis placed on direction of causality.