This article describes an intrinsic case study of project-based learning (PBL) experience involving an NGO as an external client to promote sustainability competencies. Two research questions are posed: (1) How did this experiential PBL approach impact students learning to develop sustainability competencies by incorporating a responsible engineering perspective? (2) How did college students become engaged with social and sustainable PBL projects when external clients of developing economies were involved? The project-based design involved two subjects in the second year of an Industrial engineering degree. The client was an NGO with an existing project to improve the supply chain logistics of three refugee camps managed by women. Students had to cooperatively develop a sustainable proposal for the NGO with a global mindset. Findings obtained from the analysis of the reflections of students and teachers indicate that this methodology helps students to acquire comprehensively learning outcomes and to develop sustainability competencies. Sustainable and socially responsible engineering were achieved through a methodology that considers the UN Sustainable Development Goals (SDGs) and engages students in real projects. This approach promotes student awareness on the importance of their actions and their personal behavior as engineers, including a gender perspective, while training them to move towards SDG4 and 5.