In order to combat the challenges of scarce spectrum bandwidth and energy supply in the Internet-of-Things networks, this article investigates a wireless-powered massive multiple-input-multiple-output (MIMO) underlay cognitive radio (CR) system, where the secondary user (SU) harvests the energy from the primary network through a time-switching (TS) strategy. Moreover, the detection technique of maximum-ratio combining (MRC) is applied at base stations (BSs) due to its low complexity. Thereon, the achievable rate of the secondary network is thoroughly analyzed by accounting for spatial correlations at both users and BSs, which significantly differentiates the analysis from the prior literature. With the analytical results, the impacts of the number of antennas and the spatial correlations are quantified. In particular, the negative impact of the spatial correlation on the achievable rate is theoretically proved based on the majorization theory. Furthermore, the TS factor and/or power allocation coefficients are optimally designed based on the statistical channel state information (CSI) only to maximize the achievable rate while ensuring the maximum endurable interference constraint. It is found that the optimal power allocation matrix is a variant of water-filling solution with two water levels associated with sum power constraint and sum weighted power constraint, respectively. The weighting matrix is aligned with the transmit spatial correlation in the SU. The joint design of TS factor and power allocation coefficients is also shown to reach a superior performance over the algorithms-based solely on TS factor or power allocation coefficients optimizations. Finally, the analytical results are validated by conducting simulations.