This paper presents Random Asynchronous Wakeup (RAW), a power saving technique for sensor networks that reduces energy consumption without significantly affecting the latency or connectivity of the network. RAW builds on the observation that when a region of a shared-channel wireless network has a sufficient density of nodes, only a small number of them need be active at any time to forward traffic for active connections.RAWis a distributed, randomized algorithm where nodes make local decisions on whether to sleep, or to be active. Each node is awake for a randomly chosen fixed interval per time frame. High node density results in existence of several paths between two given nodes whose path length and delay characteristics are similar to the shortest path. Thus, a packet can be forwarded to any of several nodes in order to be delivered to the destination without affecting much the path length and delay experienced by the packet when compared to when forwarded through the shortest path.Improvement in system lifetime, due to RAW, increases as the ratio of idle-to-sleep energy consumption increases, and as the density of the network increases. Through analytical and experimental evaluations, we show that RAW improves communication latency and system lifetime compared to current schemes.