This study addresses the challenge in identifying and preserving higher-order cognitive functions within a complex dynamic systems framework during neurosurgery. Traditionally, neurosurgical practice has prioritized avoiding language and motor deficits, while higher-order functions-such as social cognition and executive processes-remain underexplored. These functions arise from dynamic large-scale networks operating in an optimal balance between synchronization and metastability rather than from isolated and localized cortical regions. This complexity highlights a paradox of non-locality in awake cognitive mapping: no single area "contains" a function, but certain "critical points" can transiently disrupt network dynamics when stimulated intraoperatively. Direct electrical stimulation provides unique real-time insights by inducing brief dyssynchronizations that elicit observable behavioral changes, allowing neurosurgeons and neuropsychologists to pinpoint crucial cortical and subcortical "connectome-stop points" and minimize damage. Preserving deep white-matter tracts is essential, given their limited neuroplasticity and the profound, often irreversible impact of tract lesions on cognition. To address these challenges, we propose a three-step awake cognitive mapping approach: (1) localizing critical points of networks via DES-driven behavioral impairment, (2) constant monitoring of multiple cognitive domains as tumor resection progresses, and (3) halting resection at connectome-stop points to prevent irreversible deficits. An illustrative case involving a right parietal glioma demonstrates how this methodology integrates computational neuroscience, network theory, and clinical practice to achieve optimal functional preservation and maintain the patient's quality of life.