It is said that we lose track of time - that "time flies" - when we are engrossed in a story. How does engagement with the story cause this distorted perception of time, and what are its neural correlates? People commit both time and attentional resources to an engaging stimulus. For narrative videos, attentional engagement can be represented as the level of similarity between the electroencephalographic responses of different viewers. Here we show that this measure of neural engagement predicted the duration of time that viewers were willing to commit to narrative videos. Contrary to popular wisdom, engagement did not distort the average perception of time duration. Rather, more similar brain responses resulted in a more uniform perception of time across viewers. These findings suggest that by capturing the attention of an audience, narrative videos bring both neural processing and the subjective perception of time into synchrony.