In everyday listening situations, we need to constantly switch between alternative sound sources and engage attention according to cues that match our goals and expectations. The exact neuronal bases of these processes are poorly understood. We investigated oscillatory brain networks controlling auditory attention using cortically constrained fMRI-weighted magnetoencephalography/EEG source estimates. During consecutive trials, participants were instructed to shift attention based on a cue, presented in the ear where a target was likely to follow. To promote audiospatial attention effects, the targets were embedded in streams of dichotically presented standard tones. Occasionally, an unexpected novel sound occurred opposite to the cued ear to trigger involuntary orienting. According to our cortical power correlation analyses, increased frontoparietal/temporal 30-100 Hz gamma activity at 200-1400 msec after cued orienting predicted fast and accurate discrimination of subsequent targets. This sustained correlation effect, possibly reflecting voluntary engagement of attention after the initial cue-driven orienting, spread from the TPJ, anterior insula, and inferior frontal cortices to the right FEFs. Engagement of attention to one ear resulted in a significantly stronger increase of 7.5-15 Hz alpha in the ipsilateral than contralateral parieto-occipital cortices 200-600 msec after the cue onset, possibly reflecting cross-modal modulation of the dorsal visual pathway during audiospatial attention. Comparisons of cortical power patterns also revealed significant increases of sustained right medial frontal cortex theta power, right dorsolateral pFC and anterior insula/inferior frontal cortex beta power, and medial parietal cortex and posterior cingulate cortex gamma activity after cued versus novelty-triggered orienting (600-1400 msec). Our results reveal sustained oscillatory patterns associated with voluntary engagement of auditory spatial attention, with the frontoparietal and temporal gamma increases being best predictors of subsequent behavioral performance.