This study presents a novel event-triggered finite-time stochastic control method for a robot manipulator. The random moment of inertia of the manipulator system is expressed by building a stochastic dynamic model, and the parameter variation disturbance is estimated by using a stochastic configuration neural network. An event-triggered controller with uncertain disturbance rejection is proposed, which not only realizes the stochastic finite-time stability of the tracking error system, but also guarantees the safety of motion velocity, and robustly improves the tracking accuracy of the robot manipulator. Compared with the existing works, the obvious feature of the proposed method is that it can simultaneously solve the random disturbance and uncertain parameter disturbance of the manipulator system, save communication resources, and ensure that the manipulator system can reach a steady state in finite time. We also discuss the effectiveness of the proposed stochastic tracking control method. Simulation and comparative analysis results further show that the controller can be updated less frequently while guaranteeing robust tracking performance of the robot manipulator.