This paper highlights the need to deepen key sustainability competencies contextualized within domain-specific courses. It explores the integration of these competencies into the Diploma in Electrical and Electronics Engineering (DEEE) curriculum, leveraging the Common Core Curriculum (CCC) and the Conceive, Design, Implement, Operate (CDIO) framework already in place. The integration is guided by a flexible framework developed in Singapore Polytechnic (SP), which outlines eight key sustainability competencies: systems thinking, futures thinking, values thinking, strategic thinking, interpersonal, intrapersonal, implementation, and integrated problem-solving. This paper explains the work done, beginning with identifying the existing skills and gaps, followed by progressively introducing or enhancing these competencies within suitable domain-specific modules, aligned with the DEEE course structure, advancing from foundational to advanced levels. This paper demonstrates how these sustainability competencies are applied in practice, using a case study based on the CDIO project in a Year 2 module Microcontroller Applications (MAPP). First, it shares the results of a gap analysis on all Year 1 modules and how it can support learning MAPP. Next, it illustrates how the competencies are contextualized and applied throughout the CDIO project phases. It then outlines how the deepening of the key competencies can be achieved in Year 3 using a lifecycle approach for the Sustainable Energy Specialization track. This approach strengthens the course's alignment with sustainability education goals and demonstrates how the approach from SP, built on the CDIO framework, is used to deepen necessary sustainability competencies within a course.