Values find their full completion only in the competent behaviour of university members. The values of a university are directly linked with the competences of university teachers and, together with the principles of sustainability, are the crucial pillars of a ‘sustainability triangle’ of higher education institutions that is introduced and modelled in this paper, which examines these phenomena and the potential ties existing between them. We experimentally define the 10 principles of sustainability in higher education based on the personal academic experience of the authors as well the most frequently cited opinions in the literature. The paper subsequently presents the results of a sociological survey performed in two European countries and compares the results of Czech university students in the public security sector (n = 396) with those of Slovak university students in the IT sector (n = 246). An almost perfect correlation between student opinions from both sectors was confirmed with the use of Pearson’s product moments and an unpaired two-sample Student’s t-test. The results help to affirm all the postulated principles of sustainability and to approve the accuracy of the model presented, i.e., a Triangle of/for Sustainable Higher Education Institutions. The results obtained as well as our arguments simultaneously call on the governing bodies of ministries and universities to focus efforts on the harmonisation of personal and institutional values, opinions, principles, aspirations, and various motivations of all members of the university, i.e., students, teachers, and advisers.