Uncontrolled or improperly controlled electric vehicle (EV) charging can negatively impact electric distribution networks. In this paper, we develop a decentralized event-driven EV charging control scheme to achieve “valley-filling” (i.e., flattening demand profile during overnight charging), meanwhile meeting heterogeneous individual charging requirements and satisfying distribution network constraints. This control scheme is capable of handling EVs' random arrivals and departures. The formulated problem is an optimization problem with a non-separable objective function and strongly coupled inequality constraints. We describe a novel shrunken-primal-dual subgradient (SPDS) algorithm to support the decentralized control scheme, and verify its efficacy and convergence with a simple distribution network model.