In this article, a low-cost system for 2D eye gaze estimation with low-resolution webcam images is presented. Two algorithms are proposed for this purpose, one for the eye-ball detection with stable approximate pupil-center and the other one for the eye movements' direction detection. Eyeball is detected using deformable angular integral search by minimum intensity (DAISMI) algorithm. Deformable template-based 2D gaze estimation (DTBGE) algorithm is employed as a noise filter for deciding the stable movement decisions. While DTBGE employs binary images, DAISMI employs gray-scale images. Right and left eye estimates are evaluated separately. DAISMI finds the stable approximate pupil-center location by calculating the mass-center of eyeball border vertices to be employed for initial deformable template alignment. DTBGE starts running with initial alignment and updates the template alignment with resulting eye movements and eyeball size frame by frame. The horizontal and vertical deviation of eye movements through eyeball size is considered as if it is directly proportional with the deviation of cursor movements in a certain screen size and resolution. The core advantage of the system is that it does not employ the real pupil-center as a reference point for gaze estimation which is more reliable against corneal reflection. Visual angle accuracy is used for the evaluation and benchmarking of the system. Effectiveness of the proposed system is presented and experimental results are shown.