Humans’ remarkable capacity to flexibly adapt their behavior based on rapid situational changes is termed cognitive control. Intuitively, cognitive control is thought to be affected by the state of alertness; for example, when drowsy, we feel less capable of adequately implementing effortful cognitive tasks. Although scientific investigations have focused on the effects of sleep deprivation and circadian time, little is known about how natural daily fluctuations in alertness in the regular awake state affect cognitive control. Here we combined a conflict task in the auditory domain with EEG neurodynamics to test how neural and behavioral markers of conflict processing are affected by fluctuations in alertness. Using a novel computational method, we segregated alert and drowsy trials from two testing sessions and observed that, although participants (both sexes) were generally sluggish, the typical conflict effect reflected in slower responses to conflicting information compared with nonconflicting information, as well as the moderating effect of previous conflict (conflict adaptation), were still intact. However, the typical neural markers of cognitive control—local midfrontal theta-band power changes—that participants show during full alertness were no longer noticeable when alertness decreased. Instead, when drowsy, we found an increase in long-range information sharing (connectivity) between brain regions in the same frequency band. These results show the resilience of the human cognitive control system when affected by internal fluctuations of alertness and suggest that there are neural compensatory mechanisms at play in response to physiological pressure during diminished alertness.