Resting-state brain networks represent the intrinsic state of the brain during the majority of cognitive and sensorimotor tasks. However, no study has yet presented concise predictors of task-induced vigilance variability from spectro-spatial features of the resting-state electroencephalograms (EEG). In this study, ten healthy volunteers have participated in fixed-sequence, varying-duration sessions of sustained attention to response task (SART) for over 100 minutes. A novel and adaptive cumulative vigilance scoring (CVS) scheme is proposed based on tonic performance and response time. Multiple linear regression (MLR) using feature relevance analysis has shown that average CVS, average response time, and variabilities of these scores can be predicted (p < 0.05) from the resting-state band-power ratios of EEG signals. Cross-validated neural networks also captured different associations for narrow-band beta and wide-band gamma and differences between the high- and low-attention networks in temporal regions. The proposed framework and these first findings on stable and significant attention predictors from the power ratios of resting-state EEG can be useful in brain-computer interfacing and vigilance monitoring applications.