Speech perception is supported by both acoustic signal decomposition and semantic context. This study, using event-related functional magnetic resonance imaging, investigated the neural basis of this interaction with two speech manipulations, one acoustic (spectral degradation) and the other cognitive (semantic predictability). High compared with low predictability resulted in the greatest improvement in comprehension at an intermediate level of degradation, and this was associated with increased activity in the left angular gyrus, the medial and left lateral prefrontal cortices, and the posterior cingulate gyrus. Functional connectivity between these regions was also increased, particularly with respect to the left angular gyrus. In contrast, activity in both superior temporal sulci and the left inferior frontal gyrus correlated with the amount of spectral detail in the speech signal, regardless of predictability. These results demonstrate that increasing functional connectivity between high-order cortical areas, remote from the auditory cortex, facilitates speech comprehension when the clarity of speech is reduced.