Sustainability is increasingly present in all areas of society and organizations. In Information Technology (IT), the idea of sustainability has come through the so-called Green IT practices. These practices are attracting many organizations that have realized the importance of this area and the benefits it generates socially, economically, and environmentally. However, there is a lack of standards and/or frameworks that help organizations to carry out these Green IT practices. For this reason, we have developed the "Governance and Management Framework for Green IT" and an ISO/IEC 33000-based maturity model for this framework, which allow to perform the implementation, evaluation, and improvement of Green IT in organizations in a systematic and progressive manner. In the present study we present an empirical validation through a case study that we have conducted with these proposals, emphasizing the application of ISO/IEC 33000 family of standards to Green IT. The results obtained in this case study demonstrate the importance of having a maturity model for Green IT and the validity and usefulness of the application of ISO/IEC 33000 to Green IT through the developed maturity model.