The biophysics of nucleic acid hybridization and strand displacement have been used for the rational design of a number of nanoscale structures and functions. Recently, molecular amplification methods have been developed in the form of non-covalent DNA catalytic reactions, in which single-stranded DNA (ssDNA) molecules catalyze the release of ssDNA product molecules from multi-stranded complexes. Here, we characterize the robustness and specificity of one such strand displacement-based catalytic reaction. We show that the designed reaction is simultaneously sensitive to sequence mutations in the catalyst and robust to a variety of impurities and molecular noise. These properties facilitate the incorporation of strand displacement-based DNA components in synthetic chemical and biological reaction networks.