Accurately simulating heterogeneously catalyzed reactions requires reliable barriers for molecules reacting at defects on metal surfaces, such as steps. However, first- principles methods capable of computing these barriers to chemical accuracy have yet to be demonstrated. We show that state-resolved molecular beam experiments combined with ab initio molecular dynamics using specific reaction parameter density functional theory (SRP-DFT) can determine the molecule-metal surface interaction with the required reliability. Crucially, SRP-DFT exhibits transferability: the functional devised for methane reacting on a flat (111) face of Pt (and Ni) also describes its reaction on stepped Pt(211) with chemical accuracy. Our approach can help bridge the materials gap between fundamental surface science studies on regular surfaces and heterogeneous catalysis in which defected surfaces are important.