Registration algorithms performed on point clouds or range images of face scans have been successfully used for automatic 3D face recognition under expression variations, but have rarely been investigated to solve pose changes and occlusions mainly since that the basic landmarks to initialize coarse alignment are not always available. Recently, local feature-based SIFT-like matching proves competent to handle all such variations without registration. In this pa- per, towards 3D face recognition for real-life biometric applications, we significantly extend the SIFT-like matching framework to mesh data and propose a novel approach using fine-grained matching of 3D keypoint descriptors. First, two principal curvature-based 3D keypoint detectors are provided, which can repeatedly identify complementary locations on a face scan where local curvatures are high. Then, a ro- bust 3D local coordinate system is built at each keypoint, which allows extraction of pose-invariant features. Three key- point descriptors, corresponding to three surface differential quantities, are designed, and their feature-level fusion is employed to comprehensively describe local shapes of detected keypoints. Finally, we propose a multi-task sparse representation based fine-grained matching algorithm, which ac- counts for the average reconstruction error of probe face descriptors sparsely represented by a large dictionary of gallery descriptors in identification. Our approach is evaluated on the Bosphorus database and achieves rank-one recognition rates of 96.56%, 98.82%, 91.14%, and 99.21% on the entire database, and the expression, pose, and occlusion subsets, respectively. To the best of our knowledge, these are the best results reported so far on this database. Additionally, good generalization ability is also exhibited by the experiments on the FRGC v2.0 database.