Lately, there has been a rising trend towards integrating sustainability issues and implementing sustainable development (SD) goals into higher education, especially in the Information and Communication Technology (ICT) field. This paper presents the challenges of the introduction of education for sustainability in higher education institutions, analyzes how these challenges could be addressed, and records the essential principles that can guide the incorporation of SD education in higher education. At the same time, this paper advocates the concept of sustainability integration into undergraduate ICT curricula and provides indications for developing ICT curricula that integrate sustainability issues. This paper also examines the contribution of education to the environmental awareness of the students at a Greek University while it captures their perceptions regarding the necessity for the inclusion of sustainability in the ICT curricula. The results are based on the processing of two questionnaires (pre-test and post-test data) distributed during two lectures regarding sustainability at a two-week interval. The findings of the study prove that the direct effect of the educational intervention on the intention of the students to engage in sustainability is significant. Furthermore, it is observed that students show a positive attitude towards integrating sustainability issues into their ICT education. In addition, although students had a deficient level of understanding of the concept of SD goals before the intervention, they showed a significant increment in their previous knowledge regarding sustainability and the environmental impact of ICT studies. The research also reveals that the students are not satisfied with the engagement of the university towards sustainability, and they propose various awareness activities to support their engagement with sustainability issues in an inclusive manner.