MicroRNAs (miRNAs) have emerged as promising diagnostic biomarkers. We introduce a kinetic fingerprinting approach called single-molecule recognition through equilibrium Poisson sampling (SiMREPS) for the amplification-free counting of single unlabeled miRNA molecules, which circumvents thermodynamic limits of specificity and virtually eliminates false positives. We demonstrate high-confidence, single-molecule detection of synthetic and endogenous miRNAs in both buffer and minimally treated biofluids, as well as >500-fold discrimination between single nucleotide polymorphisms.