Routing Protocol for Low-power and Lossy Networks (RPL), the de facto standard routing protocol for the Internet of Things (IoT) administers the smooth transportation of data packets across the Wireless Sensor Network (WSN). However, the mechanism fails to address the heterogeneous nature of data packets traversing the network, as these packets may carry different classes of data with different priority statuses, some real-time (time-sensitive) while others non-real-time (delay-tolerant). The standard Objective Functions (OFs), used by RPL to create routing paths, treat all classes of data as the same, this practice is not only inefficient but results in poor network performance. In this article, the Prioritized Shortest Path Computation Mechanism (PSPCM) is proposed to resolve the data prioritization of heterogeneous data and inefficient power management issues. The mechanism prioritizes heterogeneous data streaming through the network into various priority classes, based on the priority conveyed by the data. The PSPCM mechanism routes the data through the shortest and power-efficient path from the source to the destination node. PSPCM generates routing paths that exactly meet the need of the prioritized data. It outperformed related mechanisms with an average of 91.49% PDR, and average power consumption of 1.37mW which translates to better battery saving and prolonged operational lifetime while accommodating data with varying priorities.