Individuals with schizophrenia exhibit problems in language comprehension that are most evident during discourse processing. We hypothesized that deficits in cognitive control contribute to these comprehension deficits during discourse processing, and investigated the underlying cognitive-neural mechanisms using EEG (alpha power) and ERPs (N400). N400 amplitudes to globally supported or unsupported target words near the end of stories were used to index sensitivity to previous context. ERPs showed reduced sensitivity to context in patients versus controls. EEG alpha-band activity was used to index attentional engagement while participants listened to the stories. We found that context effects varied with attentional engagement in both groups, as well as with negative symptom severity in patients. Both groups demonstrated trial-to-trial fluctuations in alpha. Relatively high alpha power was associated with compromised discourse processing in participants with schizophrenia when it occurred during any early portion of the story. In contrast, discourse processing was only compromised in controls when alpha was relatively high for longer segments of the stories. Our results indicate that shifts in attention from the story context may be more detrimental to discourse processing for participants with schizophrenia than for controls, most likely due to an impaired ability to benefit from global context.