A major practical barrier for implementing carbon-based electrode arrays with high device-packing density is to ensure large, predictable, and homogeneous sensitivities across the array. Overcoming this barrier depends on quantitative models to predict electrode sensitivity from its material structure. However, such models are currently lacking. Here, we show that the sensitivity of multilayer graphene electrodes increases linearly with the average point defect density, whereas it is unaffected by line defects or oxygen-containing groups. These quantitative relationships persist until the electrode material transitions to a fully disordered sp2 carbon, where sensitivity declines sharply. We show that our results generalize to a variety of graphene production methods and use them to derive a predictive model that guides nano-engineering graphene structure for optimum sensitivity. Our approach achieves reproducible fabrication of miniaturized sensors with extraordinarily higher sensitivity than conventional material. These results lay the foundation for new integrated electrochemical sensor arrays based on nano-engineered graphene.