Sustainability is a difficult topic, and education systems are generally complicated, including multiple levels as well as diverse organizations and actors. This dual complexity, which affects both sustainability and higher education systems, poses great challenges for research. Although there has been a growing interest in adopting sustainable practices within HEIs, few studies have focused on the integration of sustainability concerns into curricula through a process-centric lens, and the majority of studies in this area are mainly input-oriented. Therefore, in this study, we seek to address the need for a comprehensive understanding to solve local problems through process-centric views and tested methodologies, offering new possibilities for teaching sustainability. We focus on education as a system (i.e., comprising inputs, outputs, and processes) and develop a conceptual design of the deployed teaching processes for a real-world project scenario aimed at mainstreaming sustainability into the curriculum, in the case of business engineering. The research process consisted of (i) the application of a functional decomposition technique at institutional and project levels for integration of the project into current academic practices; (ii) the application of the SIPOC (Supplier, Inputs, Process, Outputs, Customer) method in conjunction with a flowcharting technique to capture the flow of interactions between project processes and the surrounding structure. The added value derives from a better understanding of the relationships between upstream and downstream processes, enabling sustained improvement and strengthening the teaching practices related to sustainability.