Both time-based (when) and feature-based (what) aspects of attention facilitate behavior, so it is natural to hypothesize additive effects. We tested this conjecture by recording response behavior and electroencephalographic (EEG) data to auditory pitch changes, embedded at different time lags in a continuous sound stream. Participants reacted more rapidly to larger rather than smaller feature change magnitudes (deviancy), as well as to changes appearing after longer rather than shorter waiting times (hazard rate of response times). However, the feature and time dimensions of attention separately contributed to response speed, with no significant interaction. Notably, phase coherence at low frequencies (delta and theta bands, 1–7 Hz) predominantly reflected attention capture by feature changes, while oscillatory power at higher frequency bands, alpha (8–12 Hz) and beta (13–25 Hz) reflected the orienting of attention in time. Power and phase coherence predicted different portions of response speed variance, suggesting a division of labor in encoding sensory attention in complex auditory scenes.