The comparison of structural subsites in proteins is increasingly relevant to the prediction of their biological function. To address this problem, we present the Match Augmentation algorithm (MA). Given a structural motif of interest, such as a functional site, MA searches a target protein structure for a match: the set of atoms with the greatest geometric and chemical similarity. MA is extremely efficient because it exploits the fact that the amino acids in a structural motif are not equally important to function. Using motif residues ranked on functional significance via the Evolutionary Trace (ET), MA prioritizes its search by initially forming matches with functionally significant residues, then, guided by ET, it augments this partial match stepwise until the whole motif is found. With this hierarchical strategy, MA runs considerably faster than other methods, and almost always identifies matches in homologs known to have cognate functional sites. Second, in order to interpret matches, we further introduce a statistical method using nonparametric density estimation of the frequency distribution of structural matches. Our results show that the hierarchy of functional importance within structural motifs speeds up the search within targets, and points to a new method to score their statistical significance.