PET and fMRI studies suggest that auditory narrative comprehension is supported by a bilateral multilobar cortical network. The superior temporal resolution of magnetoencephalography (MEG) makes it an attractive tool to investigate the dynamics of how different neuroanatomic substrates engage during narrative comprehension. Using beta-band power changes as a marker of cortical engagement, we studied MEG responses during an auditory story comprehension task in 31 healthy adults. The protocol consisted of two runs, each interleaving 7 blocks of the story comprehension task with 15 blocks of an auditorily presented math task as a control for phonological processing, working memory, and attention processes. Sources at the cortical surface were estimated with a frequency-resolved beamformer. Beta-band power was estimated in the frequency range of 16–24 Hz over 1-sec epochs starting from 400 msec after stimulus onset until the end of a story or math problem presentation. These power estimates were compared to 1-second epochs of data before the stimulus block onset. The task-related cortical engagement was inferred from beta-band power decrements. Group-level source activations were statistically compared using non-parametric permutation testing. A story-math contrast of beta-band power changes showed greater bilateral cortical engagement within the fusiform gyrus, inferior and middle temporal gyri, parahippocampal gyrus, and left inferior frontal gyrus (IFG) during story comprehension. A math-story contrast of beta power decrements showed greater bilateral but left-lateralized engagement of the middle frontal gyrus and superior parietal lobule. The evolution of cortical engagement during five temporal windows across the presentation of stories showed significant involvement during the first interval of the narrative of bilateral opercular and insular regions as well as the ventral and lateral temporal cortex, extending more posteriorly on the left and medially on the right. Over time, there continued to be sustained right anterior ventral temporal engagement, with increasing involvement of the right anterior parahippocampal gyrus, STG, MTG, posterior superior temporal sulcus, inferior parietal lobule, frontal operculum, and insula, while left hemisphere engagement decreased. Our findings are consistent with prior imaging studies of narrative comprehension, but in addition, they demonstrate increasing right-lateralized engagement over the course of narratives, suggesting an important role for these right-hemispheric regions in semantic integration as well as social and pragmatic inference processing.