Three-dimensional (3D) triangulation based on active binocular vision has increasing amounts of applications in computer vision and robotics. An active binocular vision system with non-fixed cameras needs to calibrate the stereo extrinsic parameters online to perform 3D triangulation. However, the accuracy of stereo extrinsic parameters and disparity have a significant impact on 3D triangulation precision. We propose a novel eye gaze based 3D triangulation method that does not use stereo extrinsic parameters directly in order to reduce the impact. Instead, we drive both cameras to gaze at a 3D spatial point P at the optical center through visual servoing. Subsequently, we can obtain the 3D coordinates of P through the intersection of the two optical axes of both cameras. We have performed experiments to compare with previous disparity based work, named the integrated two-pose calibration (ITPC) method, using our robotic bionic eyes. The experiments show that our method achieves comparable results with ITPC.