Underwater acoustic sensor networks find widespread applications in ocean science and engineering. High-performance routing protocols demand networks to achieve high throughput while minimizing energy consumption, which is crucial for enhancing energy utilization efficiency. Addressing this challenge, this paper proposes an Energy-Optimization Routing Protocol Based on Retransmission Timeout (EORT) in Underwater Acoustic Networks. During the route discovery phase, a backoff mechanism is utilized to respond to as many route requests as possible before replying, thereby controlling routing overhead. Additionally, an energy-balancing strategy is integrated aiming to balance network energy consumption. In the data transmission phase, a retransmission timeout mechanism is introduced for data monitoring and link validity assessment. Moreover, collision avoidance mechanisms are incorporated to mitigate collisions and enhance packet delivery ratio and throughput. Feedback information from monitoring and retransmission results is utilized in the route maintenance process to control maintenance overhead. Simulation and in-field experiments are conducted to compare EORT with the Ad Hoc On-Demand Distance Vector Routing (AODV) and Vector Based Forwarding (VBF) protocols. Simulation results demonstrate that EORT achieves improvements in both throughput and packet delivery ratio compared to AODV and VBF, with lower per-byte energy consumption. The underwater experiments further demonstrate that EORT improves throughput by 14.46%, packet delivery rate by 12.5%, and decreases energy consumption per byte by 0.02J.