In recent years, we have witnessed dramatic changes in the following two regards: First, Corporate Social Responsibility (CSR) practices have become ubiquitous in companies, and second, the challenge that Sustainable Development (SD) presents to society and to the planet has been illustrated in the United Nations’ Sustainable Development Goals (SDGs). In this context, this study aims to identify the extent to which companies address the SDGs through their CSR practices. We conducted the present research by first performing a content analysis to determine the communalities between CSR practices and the SDGs. Then, we performed a quantitative analysis to assess the performance of various companies in terms of common aspects of CSR and SDGs. The main findings are as follows: (1) Not all SDGs are related to CSR practices; (2) companies perform differently in their CSR practices and, consequently, make different contributions to the SDGs; and (3) there is little difference among company profiles regarding their performances in CSR practices towards the SDGs. The main contributions of this study are, first, that it provides a new perspective on the relationship between CSR and SD and, second, the creation of a list of what can be considered the minimum requirements for CSR practices if the SDGs are to be reached.