Wireless sensor networks (WSNs) are playing a vital role in automation, sensing and commercial applications. Key issues in WSNs are to satisfy Quality of service (QoS) parameters and to conserve energy. Some of the sensor nodes in WSN act as a single communication link to connect one group of sensor nodes to other in multi-hop environment. If nodes acting as a single communication link become dead due to low energy then this can cause network failure and nodes causing failure are called bottleneck nodes. This paper proposes an Energy and Priority Aware Scheduling (EPAS) scheme for bottleneck node avoidance. Every node has three priority queues to place packets of different priorities. Scheduling of packets is performed based on energy level threshold and priority level marked. Proposed scheme avoids bottleneck problem by scheduling packets of high priority based on energy level thresholds, if energy is critically low then low priority packets are dropped but sensor node still keep transmitting high priority packets in order to keep network alive. Proposed scheme is implemented using Network Simulator-2 (NS-2). Simulation results show that the scheme achieves 96% packet delivery ratio for highest priority packets and gives 52% improvement in packet delivery ratio, 0.309 Kbits/sec improved throughput and 5.16s less delay as compared to priority queuing.