Teacher enthusiasm is attracting growing attention in educational and learner psychology research. There is evidence that teacher enthusiasm is contagious in class and positively affects student emotions. Their fundamental role in shaping student engagement has also been well documented. However, the links -- between teacher enthusiasm and student emotions, and between student emotions and engagement -- remain underexplored in instructed second language acquisition. The present study adopted a mixed-method approach to examine the complex relationships between perceived teacher enthusiasm, emotions (enjoyment and boredom), and social-behavioral learning engagement among 2,002 learners of English as a foreign language (EFL) from 11 universities in China. Quantitative analyses showed small to large correlations between perceived teacher enthusiasm, enjoyment, boredom, and social-behavioral learning engagement. In addition, student enjoyment and boredom were found to co-mediate the relationship between perceptions of teacher enthusiasm and student social-behavioral engagement in English classes. Qualitative interviews with nine students provided insights into the potential causes of the statistical patterns. Theoretical and pedagogical implications are discussed, followed by directions for future research.