Cognitive control is a cognitive and neural mechanism that contributes to managing the complex demands of day-to-day life. Studies have suggested that functional impairments in cognitive control associated brain circuitry contribute to a broad range of higher cognitive deficits in schizophrenia. To examine this issue, we assessed functional connectivity networks in healthy adults and individuals with schizophrenia performing tasks from two distinct cognitive domains that varied in demands for cognitive control, the RiSE episodic memory task and DPX goal maintenance task. We characterized general and cognitive control-specific effects of schizophrenia on functional connectivity within an expanded frontal parietal network (FPN) and quantified network topology properties using graph analysis. Using the network based statistic (NBS), we observed greater network functional connectivity in cognitive control demanding conditions during both tasks in both groups in the FPN, and demonstrated cognitive control FPN specificity against a task independent auditory network. NBS analyses also revealed widespread connectivity deficits in schizophrenia patients across all tasks. Furthermore, quantitative changes in network topology associated with diagnostic status and task demand were observed. The present findings, in an analysis that was limited to correct trials only, ensuring that subjects are on task, provide critical insights into network connections crucial for cognitive control and the manner in which brain networks reorganize to support such control. Impairments in this mechanism are present in schizophrenia and these results highlight how cognitive control deficits contribute to the pathophysiology of this illness.