Student engagement is critical for learning and adjustment, but poor personal resources, such as low academic self-concept and mental health problems, can impede the individual's capacity to engage in academic activities. The present study's main aim was to investigate whether student-perceived emotional support from teachers in upper secondary school can compensate for the drawbacks associated with poor personal resources with respect to various dimensions of engagement (i.e., emotional engagement, behavioral engagement, and dropout intentions). With a sample of first-year upper secondary school students (n = 1379), the research questions were approached through structural equation modeling with latent interaction terms in a cross-sectional design. The results confirmed that students with poor personal resources report lower levels of emotional and behavioral engagement and stronger dropout intentions. However, interactions between academic self-concept and perceived emotional support from teachers indicated that the disadvantages associated with poor academic self-concept were less pronounced for students who perceived their teachers as highly emotionally supportive. No such compensatory effects were found with respect to mental health problems. The findings are discussed in terms of their practical implications for promoting student engagement and preventing school dropout.