Sentence comprehension is a complex task that involves both language-specific processing components and general cognitive resources. Comprehension can be made more difficult by increasing the syntactic complexity or the presentation rate of a sentence, but it is unclear whether the same neural mechanism underlies both of these effects. In the current study, we used event-related functional magnetic resonance imaging (fMRI) to monitor neural activity while participants heard sentences containing a subject-relative or object-relative center-embedded clause presented at three different speech rates. Syntactically complex object-relative sentences activated left inferior frontal cortex across presentation rates, whereas sentences presented at a rapid rate recruited frontal brain regions such as anterior cingulate and premotor cortex, regardless of syntactic complexity. These results suggest that dissociable components of a large-scale neural network support the processing of syntactic complexity and speech presented at a rapid rate during auditory sentence processing.