In challenging listening conditions, closing the eyes is a strategy with intuitive appeal to improve auditory attention and perception. On the neural level, closing the eyes increases the power of alpha oscillations (∼10 Hz), which are a prime signature of auditory attention. Here, we test whether eye closure benefits neural and behavioral signatures of auditory attention and perception. Participants (n = 22) attended to one of two alternating streams of spoken numbers with open or closed eyes in a darkened chamber. After each trial, participants indicated whether probes had been among the to-be-attended or to-be-ignored numbers. In the EEG, states of relative high versus low alpha power accompanied the presentation of attended versus ignored numbers. Importantly, eye closure did not only increase the overall level of absolute alpha power but also the attentional modulation thereof. Behaviorally, however, neither perceptual sensitivity nor response criterion was affected by eye closure. To further examine whether this behavioral null result would conceptually replicate in a simple auditory detection task, a follow-up experiment was conducted that required participants (n = 19) to detect a near-threshold target tone in noise. As in the main experiment, our results provide evidence for the absence of any difference in perceptual sensitivity and criterion for open versus closed eyes. In summary, we demonstrate here that the modulation of the human alpha rhythm by auditory attention is increased when participants close their eyes. However, our results speak against the widely held belief that eye closure per se improves listening behavior.