Low-frequency neural entrainment to rhythmic input has been hypothesized as a canonical mechanismthat shapes sensory perception in time. Neural entrainment is deemed particularly relevant for speech analysis, as it would contribute to the extraction of discrete linguistic elements from continuous acoustic signals. However, its causal influence in speech perception has been difficult to establish. Here, we provide evidence that oscillations build temporal predictions about the duration of speech tokens that affect perception. Using magnetoencephalography (MEG), we studied neural dynamics during listening to sentences that changed in speech rate. We observed neural entrainment to preceding speech rhythms persisting for several cycles after the change in rate. The sustained entrainment was associated with changes in the perceived duration of the last word’s vowel, resulting in the perception of words with different meanings. These findings support oscillatory models of speech processing, suggesting that neural oscillations actively shape speech perception.