In wake-up radio (WuR)-enabled wireless sensor networks, data communication among nodes is triggered in an on-demand manner, by either a sender or a receiver. For receiver-initiated WuR (RI-WuR), a~receiving node wakes up sending nodes through a wake-up call. Correspondingly sending nodes transmit packets in a traditional way by competing with one another multiple times in a single operational cycle. In~this paper, we propose a receiver-initiated consecutive packet transmission WuR (RI-CPT-WuR) medium access control (MAC) protocol, which eliminates multiple competitions to achieve higher energy efficiency. Furthermore, we develop two associated discrete time Markov chains (DTMCs) for evaluating the performance of RI-CPT-WuR and an existing RI-WuR MAC protocol. Using the solutions from the DTMC models, closed-form expressions for network throughput, average delay, packet reliability ratio, energy consumption and lifetime, and energy efficiency for both protocols are obtained. Numerical results demonstrate the superiority of the RI-CPT-WuR protocol.