Universities are the hope of the world to promote sustainability, in them are the necessary resources to significantly impact the awareness of citizens and in this way the territories, but how to do it with curricula designed under the paradigm of the formation of subject matter experts? This manuscript presents the case study of the Software Engineering program at the University of Cartagena. The study shows a strategy to allow the University to achieve its Mission, impact the sustainable development of territories, and improve its visibility in the National Science and Technology System. The study was conducted in 7 different municipalities of Colombia, in which the program is developed. Each territory have specific problems to address in terms of Sustainable Development and different cultures. The groups of participants were composed of 4 coordinators, 42 professors, and 205 students belonging to the program. The central problem of the study focused on how to close the gap between the fulfillment of the University’s mission and the results produced by the program. The research approach was mixed. The action research method was used following the phases of Deming’s total quality cycle. The main results achieved was the design and validation of a strategy that articulate the missionary axes of the University, while promoting sustainability in the territories and increasing scientific and technological products at university. The results suggest the strategy to promote sustainability from high education.