Although perovskite oxyhydrides (POHs) have shown promise as a support for selective hydrogenation, it is unknown if they themselves can catalyze alkyne semi-hydrogenation. Here, we use first-principles density functional theory, coupled with microkinetic modeling, to investigate acetylene semi-hydrogenation on a prototypical POH, cubic BaTiO2.5H0.5 (BTOH). Two different mechanisms are examined on a representative surface of BTOH under the reaction conditions: both are based on the Horiuti–Polanyi mechanism, but the way of H2 dissociation is different. In mechanism 1, a lattice hydride H atom and then a surface adsorbed H atom sequentially hydrogenate the adsorbed acetylene. In mechanism 2, two lattice hydride H atoms from the BTOH sequentially hydrogenate the adsorbed acetylene. In both mechanisms, the H atoms are replenished from gas phase H2 dissociation. Using density functional theory (DFT), we have calculated pathways for these two mechanisms in hydrogenation of acetylene to ethylene, as well as further to ethane. Microkinetic modeling based on the DFT energetics indicates that at 523 K, hydrogenation to ethylene and ethane via mechanism 1 occurs at a rate up to two orders of magnitude faster than via mechanism 2. A selectivity analysis for the temperature range of 373–673 K shows that the product observed is essentially only ethylene within the more active mechanism 1. This is because at the steady state, there is a significant amount of surface anion vacancies that facilitate heterolytic H2 dissociation and help stabilize a vinyl intermediate. The present findings suggest that POHs are capable of selective hydrogenation, thanks to their rich hydrogen surface-redox chemistry.