Cognitive reserve is one's mental resilience or resistance to the effects of structural brain damage. Reserve effects are well established in people with multiple sclerosis (PwMS) and Alzheimer's disease, but the neural basis of this phenomenon is unclear. We aimed to investigate whether preservation of functional connectivity explains cognitive reserve. Seventy-four PwMS and 29 HCs underwent neuropsychological assessment and 3 T MRI. Structural damage measures included gray matter (GM) atrophy and network white matter (WM) tract disruption between pairs of GM regions. Resting-state functional connectivity was also assessed. PwMS exhibited significantly impaired cognitive processing speed (t = 2.14, p = .037) and visual/spatial memory (t = 2.72, p = .008), and had significantly greater variance in functional connectivity relative to HCs within relevant networks (p < .001, p < .001, p = .016). Higher premorbid verbal intelligence, a proxy for cognitive reserve, predicted relative preservation of functional connectivity despite accumulation of GM atrophy (standardized-β = .301, p = .021). Furthermore, preservation of functional connectivity attenuated the impact of structural network WM tract disruption on cognition (β = -.513, p = .001, for cognitive processing speed; β = -.209, p = .066, for visual/spatial memory). The data suggests that preserved functional connectivity explains cognitive reserve in PwMS, helping to maintain cognitive capacity despite structural damage. © 2019 The Authors. Human Brain Mapping published by Wiley Periodicals, Inc.