Broca’s area in the posterior half of the left inferior frontal gyrus has traditionally been considered an important node in the speech production network. Nevertheless, recovery of speech production has been reported, to different degrees, within a few months of damage to Broca’s area. Importantly, contemporary evidence suggests that, within Broca’s area, its posterior part (i.e. pars opercularis) plays a more prominent role in speech production than its anterior part (i.e. pars triangularis). In this study, we therefore investigated the brain activation patterns that underlie accurate speech production following stroke damage to the opercular part of Broca’s area. By combining functional MRI and 13 tasks that place varying demands on speech production, brain activation was compared in (i) seven patients of interest with damage to the opercular part of Broca’s area; (ii) 55 neurologically intact controls; and (iii) 28 patient controls with left-hemisphere damage that spared Broca’s area. When producing accurate overt speech responses, the patients with damage to the left pars opercularis activated a substantial portion of the normal bilaterally distributed system. Within this system, there was a lesion-site-dependent effect in a specific part of the right cerebellar Crus I where activation was significantly higher in the patients with damage to the left pars opercularis compared to both neurologically intact and patient controls. In addition, activation in the right pars opercularis was significantly higher in the patients with damage to the left pars opercularis relative to neurologically intact controls but not patient controls (after adjusting for differences in lesion size). By further examining how right Crus I and right pars opercularis responded across a range of conditions in the neurologically intact controls, we suggest that these regions play distinct roles in domain-general cognitive control. Finally, we show that enhanced activation in the right pars opercularis cannot be explained by release from an inhibitory relationship with the left pars opercularis (i.e. dis-inhibition) because right pars opercularis activation was positively related to left pars opercularis activation in neurologically intact controls. Our findings motivate and guide future studies to investigate (i) how exactly right Crus I and right pars opercularis support accurate speech production after damage to the opercular part of Broca’s area and (ii) whether non-invasive neurostimulation to one or both of these regions boosts speech production recovery after damage to the opercular part of Broca’s area.