To overcome the limited energy in battery-powered wireless sensor networks (WSNs), harvested energy is considered as a potential solution to achieve autonomous systems. A power manager (PM) is usually embedded in wireless nodes to adapt the computation load by changing their wake-up interval according to the harvested energy. In order to prolong the network lifetime, the PM must ensure that every node satisfies the energy neutral operation (ENO) condition. However, when a multi-hop network is considered, changing the wake-up interval regularly may cripple the synchronization among nodes and, therefore, degrade the global system quality of service. In this paper, a wake-up variation reduction PM is proposed to solve this issue. This PM is applied for wireless nodes powered by a periodic energy source (e.g., light energy in an office) over a constant cycle of 24 h. Our PM not only follows the ENO condition, but also reduces the wake-up interval variations of WSN nodes. Based on this PM, an energy-efficient protocol, named synchronized wake-up interval MAC, is also proposed. OMNET++ simulation results using three different harvested profiles show that the data rate of a WSN node can be increased up to 65% and the latency reduced down to 57% compared with state-of-the-art PMs. Validations on a real WSN platform have also been performed and confirmed the efficiency of our approach.