Energy consumption and transmission reliability are the most common issues in wireless sensor networks (WSNs). By studying the broadcast nature of data transmission in WSNs, the mechanism of guaranteeing reliable transmission is abstracted as propagation of responsibility and availability. The responsibility and availability represent the accumulated evidence of nodes to support reliable transmission. Based on the developed mechanism, an evidence-efficient cluster head rotation strategy and algorithm are presented. Furthermore, backbone construction algorithm is studied to generate the minimum aggregation tree inside the candidate cluster heads. A minimum aggregation tree-based multihop routing scheme is also investigated, which allows the elected cluster heads to choose the optimally main path to forward data locally and dynamically. As a hybridization of the above, an evidence-efficient multihop clustering routing (EEMCR) method is proposed. The EEMCR method is simulated, validated, and compared with some previous algorithms. The experimental results show that EEMCR outperforms them in terms of prolonging network lifetime, improving transmission reliability, postponing emergence of death nodes, enhancing coverage preservation, and degrading energy consumption.