Urgent structural change is required in higher education to allow collaboration both within and across universities so that achieving a rapid sustainability transition can become the overarching and main purpose of education, research and work in society. A review of the literature reveals that fragmentation, caused by traditional hierarchical faculty and disciplinary organisation, is a major obstacle to such goals. Additionally, universities today operate under a competitive paradigm that prevents the transfer and application of available knowledge, thereby blocking the development of new knowledge and coherent future-oriented approaches. Fragmentation and competition prevent universities from pooling resources, understanding major challenges holistically and using systemic approaches to address them. Political agendas, funding priorities and existing mechanisms of dissemination and evaluation of academic activity contribute to inertia. Rather than applying fragmented sustainability goals within rigid silo structures, action for sustainability needs to be coordinated among academic actors both horizontally and diagonally. This requires spaces for strategic thinking, concertation, open discussion and knowledge sharing. The insights achieved in strong sustainability research environments need to direct efforts towards achieving a rapid sustainability transition, and priority must be given to structures, networks and research that already enable concertation and collaboration.