Robotic manipulators that have interacted with uncalibrated environments typically have limited positioning and tracking capabilities, if control tasks cannot be appropriately encoded using available features in the environments. Specifically, to perform 3-D trajectory following operations employing binocular vision, it seems necessary to have a priori knowledge on pointwise correspondence information between two image planes. However, such an assumption cannot be made for any smooth 3-D trajectories. This paper describes how one might enhance autonomous robotic manipulation for 3-D trajectory following tasks using eye-to-hand binocular visual servoing. Based on a novel encoded error, an image-based feedback control law is proposed without assuming pointwise binocular correspondence information. The proposed control approach can guarantee task precision by employing only an approximately calibrated binocular vision system. The goal of the autonomous task is to drive a tool mounted on the end-effector of the robotic manipulator to follow a visually determined smooth 3-D target trajectory in desired speed with precision. The proposed control architecture is suitable for applications that require precise 3-D positioning and tracking in unknown environments. Our approach is successfully validated in a real task environment by performing experiments with an industrial robotic manipulator.