Background: In university education, there is a need to provide students with the ability to use knowledge, and it has been shown that the cooperative model, with respect to information and communication technology (ICT), is effective. The aim of this study was to analyze the influence of an educational innovation program, based on the jigsaw technique and digitally supported tasks, on the psychological aspects, motivational climate, and academic performance of university students. Methods: A quasi-experimental study was conducted with an experimental group consisting of 100 university students (mean age: 21.84 ± 1.50 years). The motivational climate and the basic psychological needs in education, intrinsic motivation, academic self-concept, and academic performance were measured. Results: Significant increases were found in all variables after the intervention (p < 0.006-0.001), except for the variable, ego-motivational climate. The covariate perception of prior competences was significant for the model (p < 0.001). The students who had chosen a specific topic to develop with the jigsaw technique obtained a better grade than the rest of their classmates when the student's academic performance was included as a covariate (p < 0.001). Conclusions: The psychological aspects, motivational climates, and academic performances of university students improved after the implementation of an educational innovation program, based on the cooperative learning model with the jigsaw technique, and the use of digitally supported tasks.