The inferior parietal cortex (IPC) is involved in different cognitive functions including language. In line with the correlated transmitter receptor-based organization of the IPC, this part of the brain is parcellated into the rostral, the middle and the caudal clusters; however, the tripartite organization of the IPC has not been addressed in studies with a focus on cognitive control of language. Using multiband EPI, in this study we investigated how the rostral IPC contributes to this executive function in bilinguals. In doing so, we focused on the functional connectivity patterns of this part of the cortex with other brain areas in a context characterized with language engagement and disengagement that recruits the neural mechanisms of cognitive control. We found that in switching to L2, which was cognitively less demanding, the right rostral IPC had positive functional connectivity with the anterior division of the cingulate gyrus and the precentral gyrus. However, in switching to L1, which was cognitively more demanding, the right IPC rostral cluster had negative functional coupling with the postcentral gyrus and the precuneus cortex and positive connectivity with the posterior lobe of the cerebellum. In this condition, the left IPC rostral cluster had negative functional coupling with the superior frontal gyrus and the precuneus cortex. Thus, the connectivity patterns of the rostral IPC was influenced by the cognitive demand in an asymmetrical and lateral manner during cognitive control of language.