Intelligent behaviour depends on the ability to suppress inappropriate actions and resolve interference between competing responses. Recent clinical and neuroimaging evidence has demonstrated the involvement of prefrontal, parietal and premotor areas during behaviours that emphasise conflict and inhibition. It remains unclear, however, whether discrete sub-regions within this network are crucial for overseeing more specific inhibitory demands. Here we probed the functional specialisation of human prefrontal cortex by combining repetitive transcranial magnetic stimulation (rTMS) with integrated behavioural measures of response inhibition (stop-signal task) and response competition (flanker task). Participants undertook a combined stop-signal/flanker task following rTMS of the inferior frontal gyrus (IFG) or dorsal premotor cortex (dPM) in each hemisphere. Stimulation of the right IFG impaired stop-signal inhibition under conditions of heightened response competition, but did not influence the ability to suppress a competing response. In contrast, stimulation of the right dPM facilitated execution but had no effect on inhibition. Neither of these results was observed during rTMS of corresponding left-hemisphere regions. Overall, our findings are consistent with existing evidence that the right IFG is crucial for inhibitory control. The observed double-dissociation of neurodisruptive effects between the right IFG and right dPM further implies that response inhibition and execution rely on distinct neural processes, despite activating a common cortical network.