Speech perception may be underpinned by a hierarchical cortical system, which attempts to match “external” incoming sensory inputs with “internal” top-down predictions. Prior knowledge modulates internal predictions of an upcoming stimulus and exerts its effects in temporal and inferior frontal cortex. Here, we used source-space magnetoencephalography (MEG) to study the spatiotemporal dynamics underpinning the integration of prior knowledge in the speech processing network. Prior knowledge was manipulated to i) increase the perceived intelligibility of speech sentences, and ii) dissociate the perceptual effects of changes in speech intelligibility from acoustical differences in speech stimuli. Cortical entrainment to the speech temporal envelope, which accounts for neural activity specifically related to sensory information, was affected by prior knowledge: This effect emerged early (˜50 ms) in left inferior frontal gyrus (IFG) and then (˜100 ms) in Heschl's gyrus (HG), and was sustained until latencies of ˜250 ms. Directed transfer function (DTF) measures were used for estimating direct Granger causal relations between locations of interest. In line with the cortical entrainment result, this analysis indicated that prior knowledge enhanced top-down connections from left IFG to all the left temporal areas of interest – namely HG, superior temporal sulcus (STS), and middle temporal gyrus (MTG). In addition, intelligible speech increased top-down information flow between left STS and left HG, and increased bottom-up flow in higher-order temporal cortex, specifically between STS and MTG. These results are compatible with theories that explain this mechanism as a result of both ascending and descending cortical interactions, such as predictive coding. Altogether, this study provides a detailed view of how, where and when prior knowledge influences continuous speech perception.