There has been increasing research on pedagogical approaches, sustainability competences, and how to connect them in Higher Education Institutions (HEIs). This paper's aim is to provide deeper insights into the system of pedagogical approaches and sustainability competences, as well as how these interrelate. A survey was developed to investigate sustainability teaching in 15 HEIs. The survey was sent to educators of each HEI from which 668 responses were obtained. The responses were analysed in a five-step process: (1) descriptive statistics; (2) Pearson correlations; (3) principal component analyses (PCAs) to detect groups; (4) Pearson correlations between the groups; and (5) regressions. The first step provided the base to carry out the PCAs, from which three groups for the pedagogical approaches (Universal, Social, and Environmental) and three for the sustainability competences (Extrospective-social, Introspective-personal, and Cogitative-processual) were obtained. The correlations between the groups showed that: (1) the competences are closely interrelated; (2) the pedagogical approaches are somehow interrelated; and (3) the pedagogical approaches are somehow interrelated to the competences. The regressions showed that the Universal and Social groups would be most suitable to develop all the competences' groups. The Environmental group develops only the cogitative-processual competences' group. The results served as bases to propose the Sustainability Teaching System (STS), which provides deeper insights into the system of pedagogical approaches and sustainability competences by grouping them, as well as showing directionality and strength. To improve sustainability teaching, it is necessary to understand the pedagogical approaches' groups and how they can develop the competences' groups.