Subjective experience suggests that we are able to direct our auditory attention independent of our visual gaze, e.g when shadowing a nearby conversation at a cocktail party. But what are the consequences at the behavioural and neural level? While numerous studies have investigated both auditory attention and visual gaze independently, little is known about their interaction during selective listening. In the present EEG study, we manipulated visual gaze independently of auditory attention while participants detected targets presented from one of three loudspeakers. We observed increased response times when gaze was directed away from the locus of auditory attention. Further, we found an increase in occipital alpha-band power contralateral to the direction of gaze, indicative of a suppression of distracting input. Finally, this condition also led to stronger central theta-band power, which correlated with the observed effect in response times, indicative of differences in top-down processing. Our data suggest that a misalignment between gaze and auditory attention both reduce behavioural performance and modulate underlying neural processes. The involvement of central theta-band and occipital alpha-band effects are in line with compensatory neural mechanisms such as increased cognitive control and the suppression of task irrelevant inputs.