Humans are remarkably capable of adapting their behaviour flexibly based on rapid situational changes: a capacity termed cognitive control. Intuitively, cognitive control is thought to be affected by the state of alertness, for example, when sleepy or 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 fluctuations in alertness in the regular awake state affect cognitive control. Here we combined a conflict task in the auditory domain with neurodynamics -EEG recordings- to test how neural and behavioural markers of conflict processing are affected by fluctuations in arousal. Using a novel computational method, we segregated alert and drowsy trials from a three hour testing session and observed that, although participants were generally slower, the typical slower responses to conflicting information, compared to non-conflicting information, was still intact, as well as the effect of previous trials (i.e. conflict adaptation). However, the behaviour was not matched by the typical neural markers of cognitive control -local medio-frontal theta-band power changes-, that participants showed during full alertness. Instead, a decrease in power of medio-frontal theta was accompanied by an increase in long-range information sharing (connectivity) between brain regions in the same frequency band. The results show the resilience of the human cognitive control system when affected by internal fluctuations of our arousal state and suggests a neural compensatory mechanism when the system is under physiological pressure due to diminished alertness.