Over forty years have passed since the first evidence showing the unbalanced attentional allocation of humans across the two visual fields, and since then, a wealth of behavioral, neurophysiological, and clinical data increasingly showed a right hemisphere dominance for orienting of attention. However, inconsistent evidence exists regarding the right-hemisphere dominance for executive control of attention, possibly due to a lack of consideration of its dynamics with the alerting and orienting functions. In this study, we used a version of the Attentional Network Test with lateralized presentation of the stimuli to the left visual field (processed by the right hemisphere, RH) and right visual field (processed by the left hemisphere, LH) to examine visual field differences in executive control of attention under alerting and orienting of attention. Analyses of behavioral performance (reaction time and error rate) showed a more efficient executive control (reduced conflict effect) in the RH compared to the LH for the reaction time, under conditions of increased alerting and of informative spatial orienting. These results demonstrate the right-hemisphere superiority for executive control, and that this effect depends on the involvement of the alerting and orienting functions.