Minute-scale fluctuations in the normalized EEG log spectrum, when correlated with concurrent changes in level of performance on a sustained auditory detection task, showed that a single principal component of EEG spectral variance is linearly related to minute-scale changes in detection performance. The particular EEG frequencies at which this coupling is expressed are similar for most subjects under a range of task conditions, and match those recently reported from analysis of verbal self-reports during drowsiness. The one-dimensional relationship between detection performance and the EEG spectrum confirms quantitatively the intuitive assumption that minute-scale changes in behavioral alertness during drowsiness are predominantly linked to changes in global brain dynamics along a single dimension of psychophysiological arousal.