In this paper, we present a novel control strategy for the stabilization of a planar three-link underactuated manipulator with a passive first joint. Unlike other work relying on the modification of the planar robot characteristics through the inclusion of a spring or a brake, our method can stabilize the underactuated manipulator in the joint space without the inclusion of these appendages. Using the property of the partial integrability of the dynamic system, we formulate the stabilization task as a control problem for a 3-state and 2-input underactuated kinematics system. Due to the loss of full-state controllability in the resulting underactuated system, we further transform it into a chained form and propose a null space avoidance control framework to provide time-invariant feedback stabilization for the underactuated system. Finally, using the inverse chained form transformation, the original reduced system can be stabilized in terms of the manipulator configuration. Simulations were performed to demonstrate the effectiveness of the proposed control strategy.