Self-healing "smart grids" are characterized by fast-acting, intelligent control mechanisms that minimize power disruptions during outages. The corrective actions adopted during outages in power distribution networks include reconfiguration through switching control and emergency load shedding. The conventional decision-making models for outage mitigation are, however, not suitable for "smart grids" due to their slow response and computational inefficiency. Here, we present a new reinforcement learning (RL) model for outage management in the distribution network to enhance its resilience. The distinctive characteristic of our approach is that it explicitly accounts for the underlying network topology and its variations with switching control, while also capturing the complex interdependencies between state variables (along nodes and edges) by modeling the task as a graph learning problem. Our model learns the optimal control policy for power restoration using a Capsule-based graph neural network. We validate our model on two test networks, namely the 13 and 34-bus modified IEEE networks where it is shown to achieve near-optimal, real-time performance with up to 5 orders of magnitude improvement in computational speed. The resilience improvement of our model in terms of loss of energy is 4.204 MWs and 13.522 MWs for 13 and 34 buses, respectively. Our model also demonstrates generalizability across a broad range of outage scenarios.