In this study we modelled possible causes and consequences of student burnout and engagement on academic efficacy and dropout intention in university students. Further we asked, can student engagement protect against the effects of burnout? In total 4,061 university students from Portugal, Brazil, Mozambique, the United Kingdom, the United States of America, Finland, Serbia, and Macao SAR, Taiwan participated in this study. With the data collected we analyzed the influence of Social Support, Coping Strategies, and school/ course related variables on student engagement and burnout using structural equation modeling. We also analyzed the effect of student engagement, student burnout, and their interaction, on Academic Performance and Dropout Intention. We found that both student engagement and burnout are good predictors of subjective academic performance and dropout intention. However, student burnout suppresses the effect of student engagement on these variables. This result has strong implications for practitioners and administrators. To prevent student dropout, it is not enough to promote student engagement—additionally, and importantly, levels of student burnout must be kept low. Other variables such as social support and coping strategies are also relevant predictors of student engagement and burnout and should be considered when implementing preventive actions, self-help and guided intervention programs for college students.