Wireless body area network (WBAN) has become a promising network for continuous health monitoring of various diseases. The limited energy of sensors in WBAN cannot support the long-term work with the high requirements of Quality of Service (QoS) for health applications. Energy harvesting (EH)- powered WBAN, which can provide uninterrupted work, has attracted more attention from both academic and industry. However, the time-varying and heterogeneous EH states of different sensors become an important factor when designing the resource allocation schemes in EH-powered WBAN. In this paper, we propose a novel two-phase resource allocation scheme, which optimizes the allocation of the transmission power, the source rate and the time slots to improve the QoS performances of EH-powered WBAN. In the first phase, we investigate the statistical knowledge of energy harvesting to measure the longterm QoS performances, and then a joint Power-Rate Control Scheme (PRCS) is proposed to optimize the transmission power and the source rate for ensuring the long-term QoS performance. Moreover, we design a QoS Aware Slot Allocation Scheme (QASAS) to dynamically adjust the time slot allocation to cope with the time-varying and heterogeneous EH states for obtaining better short-term QoS performances in the second phase. Finally, numerical simulation results demonstrate that the proposed joint Power-Rate-Slot Resource Allocation scheme (PRS-RA) of EHpowered WBANs can efficiently exploit the time-varying EH to improve both the long-term and short-term QoS performances.