We present a novel discriminative regression based approach for the Constrained Local Models (CLMs) framework, referred to as the Discriminative Response Map Fitting (DRMF) method, which shows impressive performance in the generic face fitting scenario. The motivation behind this approach is that, unlike the holistic texture based features used in the discriminative AAM approaches, the response map can be represented by a small set of parameters and these parameters can be very efficiently used for reconstructing unseen response maps. Furthermore, we show that by adopting very simple off-the-shelf regression techniques, it is possible to learn robust functions from response maps to the shape parameters updates. The experiments, conducted on Multi-PIE, XM2VTS and LFPW database, show that the proposed DRMF method outperforms state-of-the-art algorithms for the task of generic face fitting. Moreover, the DRMF method is computationally very efficient and is real-time capable. The current MATLAB implementation takes 1 second per image. To facilitate future comparisons, we release the MATLAB code and the pre-trained models for research purposes.