In this article, the performance of simultaneous wireless information and power transfer (SWIPT) in downlink (DL) Internet of Things (IoT) networks relying on the cell-free massive multiple-input–multiple-output (CF-mMIMO) technique is investigated. In such a network, the access points (APs) beam the radio-frequency (RF) energy toward IoT sensors during the DL wireless power transfer phase. Tight closed-form expressions for DL harvested energy (HE) and achievable rate with conjugate beamforming (CB) and normalized CB (NCB) are, respectively, derived, which enable us to analyze the behaviors of CB and NCB schemes in terms of both HE and achievable rate. Apart from this, to guarantee sensor fairness with respect to the HE and achievable rate, a max–min power control strategy based on the accelerated projected gradient (APG) method is proposed. Specifically, the proposed APG-based power control is able to determine the optimal solution in closed form and is more memory efficient than the convex-solver-based counterpart. These analytical results as well as the effectiveness of the proposed power control policy are verified by experimental simulations.