Eye gaze as a form of input was primarily developed for users who are unable to use usual interaction devices such as keyboard and the mouse; however, with the increasing accuracy in eye gaze detection with decreasing cost of development, it tends to be a practical interaction method for able-bodied users in soon future as well. This paper explores a low-cost, robust, rotation and illumination independent eye gaze system for gaze enhanced user interfaces. We introduce two brand-new algorithms for fast and sub-pixel precise pupil center detection and 2D Eye Gaze estimation by means of deformable template matching methodology. In this paper, we propose a new algorithm based on the deformable angular integral search algorithm based on minimum intensity value to localize eyeball (iris outer boundary) in gray scale eye region images. Basically, it finds the center of the pupil in order to use it in our second proposed algorithm which is about 2D eye gaze tracking. First, we detect the eye regions by means of Intel OpenCV AdaBoost Haar cascade classifiers and assign the approximate size of eyeball depending on the eye region size. Secondly, using DAISMI (Deformable Angular Integral Search by Minimum Intensity) algorithm, pupil center is detected. Then, by using the percentage of black pixels over eyeball circle area, we convert the image into binary (Black and white color) for being used in the next part: DTBGE (Deformable Template based 2D Gaze Estimation) algorithm. Finally, using DTBGE algorithm, initial pupil center coordinates are assigned and DTBGE creates new pupil center coordinates and estimates the final gaze directions and eyeball size. We have performed extensive experiments and achieved very encouraging results. Finally, we discuss the effectiveness of the proposed method through several experimental results.