Mental set switching is a key facet of executive control measured behaviorally through reaction time or accuracy (i.e., ‘switch costs’) when shifting among task types. One of several experimentally-dissociable influences on switch costs is ‘task set inertia’, conceptualized as the residual interference conferred when a previous stimulus-response tendency interferes with subsequent stimulus processing on a new task. Task set inertia is thought to represent the passive decay of the previous stimulus-response set from working memory, and its effects decrease with increased interstimulus interval. Closely spaced trials confer high task set inertia, while sparsely spaced trials confer low task set inertia. This functional magnetic resonance imaging (fMRI) study characterized, for the first time, two opposing brain systems engaged to resolve task set inertia: 1) a frontoparietal ‘cortical control’ network for overcoming high task set inertia interference and 2) a subcortical-motor network more active during trials with low task set inertia. These networks were distinct from brain regions showing general switching effects (i.e., switch > non-switch) and from other previously-characterized interference effects. Moreover, there were ongoing maturational effects throughout adolescence for the brain regions engaged to overcome high task set inertia not seen for generalized switching effects. These novel findings represent a new avenue of exploration of cognitive set switching neural function.