Designing a lifetime-maximization routing in wireless sensor networks poses a great challenge mainly due to unreliable wireless links and limited power supply. Recently, two natural advantages of opportunistic routing, i.e., path diversity and the improvement of transmission reliability, are exploited to develop a lifetime-extended opportunistic routing for wireless sensor networks. Besides, asynchronous sleep-wake scheduling is an effective mechanism to reduce energy consumption by appropriately arranging sensor nodes to sleep. Hence, in this paper, we propose a joint design of asynchronous sleep-wake schedules and opportunistic routing, called ASSORT, to maximize the network lifetime. Simulation results show that ASSORT effectively achieves network lifetime extension compared with other routing schemes.