This study examines the impact of academic emotions—both epistemic and achievement-related—on student engagement and performance in a first-year university course. Specifically, it investigates the interplay between epistemic emotions, e-tutorial trace data, and achievement emotions within the context of a mandatory introductory mathematics and statistics course. Epistemic emotions, such as curiosity, confusion, frustration, and surprise, play a vital role in cognitive engagement and knowledge retention but are often overshadowed by achievement emotions like anxiety, boredom, hopelessness, and enjoyment. Using dispositional learning analytics, we analyse data from six cohorts of first-year students in the Netherlands to explore how these emotions influence students' engagement with e-tutorials and their subsequent academic performance. Our findings underscore the critical role of epistemic emotions in shaping learning behaviours and achievement emotions, which in turn affect overall academic outcomes. Academic emotions were assessed using the Achievement Emotions Questionnaire (AEQ) and the Epistemic Emotion Scales (EES). Statistical analyses, including ANOVA and structural equation modelling, reveal that epistemic emotions and behavioural data from e-tutorials are strong predictors of achievement emotions and performance, with notable gender differences in both mean levels and functional patterns. This research highlights the need for a more comprehensive approach to studying academic emotions, emphasizing the significance of both epistemic and achievement emotions in fostering academic success and student well-being.