Oscillatory activity in sensory cortices reflects changes in local excitation-inhibition balance, and recent work suggests that phase signatures of ongoing oscillations predict the perceptual detection of subsequent stimuli. Low-frequency oscillations are also entrained by dynamic natural scenes, suggesting that the chance of detecting a brief target depends on the relative timing of this to the entrained rhythm. We tested this hypothesis in humans by implementing a cocktail-party-like scenario requiring subjects to detect a target embedded in a cacophony of background sounds. Using EEG to measure auditory cortical oscillations, we find that the chance of target detection systematically depends on both power and phase of theta-band (2-6 Hz) but not alpha-band (8-12 Hz) oscillations before target. Detection rates were higher and responses faster when oscillatory power was low and both detection rate and response speed were modulated by phase. Intriguingly, the phase dependency was stronger for miss than for hit trials, suggesting that phase has a inhibiting but not ensuring role for detection. Entrainment of theta range oscillations prominently occurs during the processing of attended complex stimuli, such as vocalizations and speech. Our results demonstrate that this entrainment to attended sensory environments may have negative effects on the detection of individual tokens within the environment, and they support the notion that specific phase ranges of cortical oscillations act as gatekeepers for perception.