Cortical resources are typically engaged for balance and mobility in older adults, but these resources are impaired post-stroke. Although slowed balance and mobility after stroke have been well-characterized, the effects of unilateral cortical lesions due to stroke on neuromechanical control of balance is poorly understood. Our central hypothesis is that stroke impairs the ability to rapidly and effectively engage the cerebral cortex during balance and mobility behaviors, resulting in asymmetrical contributions of each limb to balance control. Using electroencephalography (EEG), we assessed cortical N1 responses evoked over fronto-midline regions (Cz) during balance recovery in response to backward support-surface perturbations loading both legs, as well as posterior-lateral directions that preferentially load the paretic or nonparetic leg. Cortical N1 responses were smaller and delayed in the stroke group. While older adults exhibited weak or absent relationships between cortical responses and clinical function, stroke survivors exhibited strong associations between slower N1 latencies and slower walking, lower clinical mobility, and lower balance function. We further assessed kinetics of balance recovery during perturbations using center of pressure rate of rise. During backward support-surface perturbations that loaded the legs bilaterally, balance recovery kinetics were not different between stroke and control groups and were not associated with cortical response latency. However, lateralized perturbations revealed slower kinetic reactions during paretic loading compared to controls, and to non-paretic loading within stroke participants. Individuals post stroke had similar nonparetic-loaded kinetic reactions to controls implicating that they effectively compensate for impaired paretic leg kinetics when relying on the non-paretic leg. In contrast, paretic-loaded balance recovery revealed time-synchronized associations between slower cortical responses and slower kinetic reactions only in the stroke group, potentially reflecting the limits of cortical engagement for balance recovery revealed within the behavioral context of paretic motor capacity. Overall, our results implicate individuals after stroke may be uniquely limited in their balance ability by the slowed speed of their cortical engagement, particularly under challenging balance conditions that rely on the paretic leg. We expect this neuromechanical insight will enable progress toward an individualized framework for the assessment and treatment of balance impairments based on the interaction between neuropathology and behavioral context.