In recent years, the ML community has seen surges of interest in both adversarially robust learning and implicit layers, but connections between these two areas have seldom been explored. In this work, we combine innovations from these areas to tackle the problem of N-k security-constrained optimal power flow (SCOPF). N-k SCOPF is a core problem for the operation of electrical grids, and aims to schedule power generation in a manner that is robust to potentially $k$ simultaneous equipment outages. Inspired by methods in adversarially robust training, we frame N-k SCOPF as a minimax optimization problem -- viewing power generation settings as adjustable parameters and equipment outages as (adversarial) attacks -- and solve this problem via gradient-based techniques. The loss function of this minimax problem involves resolving implicit equations representing grid physics and operational decisions, which we differentiate through via the implicit function theorem. We demonstrate the efficacy of our framework in solving N-3 SCOPF, which has traditionally been considered as prohibitively expensive to solve given that the problem size depends combinatorially on the number of potential outages.