Understanding what (and to what extent) psychological factors affect university performance has attracted a lot of research interest recently. In this paper, we use logistic regression models to study the incremental predictive power of positive psychological factors over pre-enrollment achievement measures on academic performance. The study is based on the data of 302 business and economics undergraduate students from the Budapest University of Technology and Economics. Coping proved to be the most important factor that sheds light on the importance of stress management for students. We also found that using properly chosen psychological factors measuring coping, personality traits, psychological immune system, emotional intelligence, and PERMA (P—positive emotion, E—engagement, R—relationships, M—meaning, A—accomplishments) factors, together with the university entrance score and academic performance can be predicted significantly better than solely relying on pre-enrollment achievement measures.