Past cognitive neuroscience studies using naturalistic stimuli have considered narratives holistically and focused on cognitive processes. In this study, we incorporated the narrative structure, the dramatic arc, as an object of investigation, to examine how engagement levels fluctuate across a narrative-aligned dramatic arc. We explored the possibility of predicting self-reported engagement ratings from neural activity and investigated the idiosyncratic effects of each phase of the dramatic arc on brain responses as well as the relationship between engagement and brain responses. We presented a movie excerpt following the six-phase narrative arc structure to female and male participants while collecting EEG signals. We then asked this group of participants to recall the excerpt, another group to segment the video based on the dramatic arc model, and a third to rate their engagement levels while watching the movie. The results showed that the self-reported engagement ratings followed the pattern of the narrative dramatic arc. Moreover, while EEG amplitude could not predict group-averaged engagement ratings, other features comprising dynamic intersubject correlation (dISC), including certain frequency bands, dynamic functional connectivity patterns and graph features were able to achieve this. Furthermore, neural activity in the last two phases of the dramatic arc significantly predicted engagement patterns. This study is the first to explore the cognitive processes behind the dramatic arc and its phases. By demonstrating how neural activity predicts self-reported engagement, which itself aligns with the narrative structure, this study provides insights on the interrelationships between narrative structure, neural responses, and viewer engagement.