This paper investigates the age of information (AoI)-based online scheduling in multi-sensor wireless powered communication networks (WPCNs) for time-sensitive Internet of Things (IoT). Specifically, we consider a typical WPCN model, where a wireless power station (WPS) charges multiple sensor nodes (SNs) by wireless power transfer (WPT), and then the SNs are scheduled in the time domain to transmit their sampled status information with their harvested energy to a mobile edge server (MES) for decision making. For such a system, we first derive a closed-form expression of the successful data transmission probability in Nakagami-m fading channels. To pursue an efficient online scheduling policy that minimizes the Expected Weighted Sum AoI (EWSAoI) of the system, a discrete-time scheduling problem is formulated. As the problem is non-convex with non-explicit expression of the EWSAoI, we propose a Max-Weight policy based on the Lyapunov optimization theory, which schedules the SNs at the beginning of each time in terms of the one-slot conditional Lyapunov Drift. Simulations demonstrate our presented theoretical results and show that our proposed scheduling policy outperforms other baselines such as greedy policy and random round-robin (RR) policy. Especially, when the number of SNs is relatively small, the gain achieved by the proposed policy compared to the greedy policy is considerable. Moreover, some interesting insights are also observed: 1) as the number of SNs increases, the EWSAoI also increases; 2) when the transmit power is relatively small, the larger the number of SNs, the smaller the EWSAoI; 3) the EWSAoI decreases with the increment of transmit power of the WPS and then tends to be flat; 4) the EWSAoI increases with the increment of the distance between the SNs and the MES.