Autism spectrum disorder (ASD) is associated with difficulty in processing speech in a noisy background, but the neural mechanisms that underlie this deficit have not been mapped. To address this question, we used magnetoencephalography to compare the cortical responses between ASD and typically developing (TD) individuals to a passive mismatch paradigm. We repeated the paradigm twice, once in a quiet background, and once in the presence of background noise. We focused on both the evoked mismatch field (MMF) response in temporal and frontal cortical locations, and functional connectivity with spectral specificity between those locations. In the quiet condition, we found common neural sources of the MMF response in both groups, in the right temporal gyrus and inferior frontal gyrus (IFG). In the noise condition, the MMF response in the right IFG was preserved in the TD group, but reduced relative to the quiet condition in ASD group. The MMF response in the right IFG also correlated with severity of ASD. Moreover, in noise, we found significantly reduced normalized coherence (deviant normalized by standard) in ASD relative to TD, in the beta band (14–25 Hz), between left temporal and left inferior frontal sub‐regions. However, unnormalized coherence (coherence during deviant or standard) was significantly increased in ASD relative to TD, in multiple frequency bands. Our findings suggest increased recruitment of neural resources in ASD irrespective of the task difficulty, alongside a reduction in top‐down modulations, usually mediated by the beta band, needed to mitigate the impact of noise on auditory processing. Autism Res 2016,. © 2016 International Society for Autism Research, Wiley Periodicals, Inc. Autism Res 2017, 10: 631–647. © 2016 International Society for Autism Research, Wiley Periodicals, Inc.