The identity and reversibility of the elementary steps required for catalytic combustion of dimethyl ether (DME) on Pt clusters were determined by combining isotopic and kinetic analyses with density functional theory estimates of reaction energies and activation barriers to probe the lowest energy paths. Reaction rates are limited by C-H bond activation in DME molecules adsorbed on surfaces of Pt clusters containing chemisorbed oxygen atoms at near-saturation coverages. Reaction energies and activation barriers for C-H bond activation in DME to form methoxymethyl and hydroxyl surface intermediates show that this step is more favorable than the activation of C-O bonds to form two methoxides, consistent with measured rates and kinetic isotope effects. This kinetic preference is driven by the greater stability of the CH3OCH2* and OH* intermediates relative to chemisorbed methoxides. Experimental activation barriers on Pt clusters agree with density functional theory (DFT)-derived barriers on oxygen-covered Pt(111). Measured DME turnover rates increased with increasing DME pressure, but decreased as the O2 pressure increased, because vacancies (*) on Pt surfaces nearly saturated with chemisorbed oxygen are required for DME chemisorption. DFT calculations show that although these surface vacancies are required, higher oxygen coverages lead to lower C-H activation barriers, because the basicity of oxygen adatoms increases with coverage and they become more effective in hydrogen abstraction from DME. Water inhibits reaction rates via quasi-equilibrated adsorption on vacancy sites, consistent with DFT results indicating that water binds more strongly than DME on vacancies. These conclusions are consistent with the measured kinetic response of combustion rates to DME, O2, and H2O, with H/D kinetic isotope effects, and with the absence of isotopic scrambling in reactants containing isotopic mixtures of 18O2-16O2 or 12CH3O12CH3-13CH3O13CH3. Turnover rates increased with Pt cluster size, because small clusters, with more coordinatively unsaturated surface atoms, bind oxygen atoms more strongly than larger clusters and exhibit lower steady-state vacancy concentrations and a consequently smaller number of adsorbed DME intermediates involved in kinetically relevant steps. These effects of cluster size and metal-oxygen bond energies on reactivity are ubiquitous in oxidation reactions requiring vacancies on surfaces nearly saturated with intermediates derived from O2.