Adolescence is a period of heightened sensitivity to incentives and relatively weak cognitive control, which may contribute to risky behaviors. Studies of brain activity have generally identified greater activation of the ventral striatum to rewards and less activation of prefrontal regions during control tasks in adolescents compared to adults. Little is known, however, about age-related changes in the functional brain networks underlying incentive processing and cognitive control. This cross-sectional study characterized the effects of incentives on inhibitory control during an oculomotor task using whole-brain functional connectivity analyses. During an fMRI scan, one hundred forty typically developing individuals completed an incentivized antisaccade task consisting of incentive cue, preparation, and response phases. We found that task modulation of control networks increased gradually from childhood to adulthood, whereas a network including ventral striatum and ventromedial prefrontal cortex displayed an adolescent-specific peak in response to the receipt of outcomes, consistent with dual-systems models. Notably, however, greater modulation of salience and motor networks during the preparation phase mediated age-related improvements in antisaccade accuracy, whereas adolescent enhancement of value-related circuitry did not. Relative to neutral cues, both reward and loss cues enhanced task-related connectivity of the salience network when preparing to inhibit a saccade. Altogether, our findings suggest that incentives facilitate inhibitory control by enhancing the salience of one's responses and that over development, the recruitment of functional networks involved in saliency and motor preparation supports better performance.