Feature matching is a challenging problem lying at the heart of numerous computer graphics and computer vision applications. We present here the SuperMatching algorithm for finding correspondences between two sets of features. It does so by considering triangles or higher-order tuples of points, going beyond the pointwise and pairwise approaches typically used. SuperMatching is formulated using a supersymmetric tensor representing an affinity metric which takes into account feature similarity and geometric constraints between features: feature matching is cast as a higher-order graph matching problem. SuperMatching takes advantage of supersymmetry to devise an efficient sampling strategy to estimate the affinity tensor, as well as to store the estimated tensor compactly. Matching is performed by an efficient higher-order power iteration approach which takes advantage of this compact representation. Experiments on both synthetic and real captured data show that SuperMatching provides more accurate feature matching than other state-of-the-art approaches for a wide range of 2D and 3D features, with competitive computational cost.