This paper is focused on the teaching of the competences and capabilities required by the people in order to build societies characterized by the sustainability of their development. A study is presented that shows how the concept of competence, which is an abstract concept, can be translated to specific objectives in order to facilitate the educational treatment required by the teaching of competences in sustainability in the framework of the teachinglearning process. It proposes a basic competential matrix built on the four competences in sustainability considered key by the Unesco: critical analysis, systemic reflection, collaborative decision taking, and sense of responsibility with the present and future generations. Each of these competencies is the result of a plurality of factors, which are composed of different capabilities shown by the subject in observable behaviors (learning achievements). The matrix is completed with four rubrics that, as an example, contain the achievement indicators (evidences) in the performance of the corresponding competence for the higher education level. These rubrics are conceived as an instrument at the service of self-regulated learning, which is essential in the distance learning systems but also necessary in a quality education in any reference model. The proposal is open and versatile, and can be adapted to different contexts and circumstances. It aims to contribute to the processes for embedding sustainability in the curricula (curriculum greening), which, in the framework of the education for sustainable development, the teachers of all education levels from schools to universities are expected to finalize.