In recent years, the Underwater Internet of Things (IoUT) has become a popular technology for exploring the underwater environment. IoUT enables administrators to explore and monitor underwater environmental phenomena from anywhere in the world where there is Internet access. Due to the harsh underwater environment, the reliability of communication between sensor nodes deteriorates, causing certain performance issues such as higher packet loss rate and long end-to-end delay. Therefore, it is essential to manage the communications between the sensors to address these problems in order to improve the QoS. Software-defined networking (SDN) is one of the most promising architectures for providing efficient network management by decoupling the data plane from the control plane of the network. This paper proposes a new QoS routing technique for SDN-based IoUT aiming at improving QoS by establishing reliable paths between sensor nodes. To do this, the controller gathers the 3D coordinates of each underwater sensor in order to compute the distance between the nodes. Then, it estimates the reliability of each link by using underwater acoustic equations. Finally, it calculates the most reliable path with minimum delay and installs the path on the nodes located along it. The experimental results show that our mechanism significantly outperforms other non-SDN approaches in terms of several performance measures ranging from packet loss ratio and end-to-end delay to energy consumption.