An autonomous robotic nut tightening system for a serial manipulator equipped with a parallel gripper is proposed. The system features a hierarchical motion-primitive-based planner and a control-switching scheme that alternates between force and position control. Extensive simulations demonstrate the system's robustness to variance in initial conditions. Additionally, the proposed controller tightens threaded screws 14% faster than the baseline while applying 40 times less contact force on manipulands. For the benefit of the research community, the system's implementation is open-sourced.