Oxidation catalysis on reducible oxide-supported small metal clusters often involves lattice oxygen. The present work aims at differentiating whether the reaction takes place at the cluster/support interface or on the cluster. To that purpose, we trace the path of lattice oxygen from Fe3O4(001) onto small Pt clusters during the CO oxidation. While oxygen vacancies form on many other supports, magnetite maintains its surface stoichiometry upon reduction thanks to high cation mobility. To investigate whether size-dependent oxygen affinities play a role, we study two specific cluster sizes, Pt-5 and Pt-19. By separating different reaction steps in our experiment, migrating lattice oxygen can be accumulated on the clusters. Temperature-programmed desorption (TPD) and sophisticated pulsed valve experiments indicate that CO oxidation occurs with this highly reactive oxygen on the Pt clusters. Scanning tunneling microscopy (STM) shows a decrease in the apparent height of the clusters, which density functional theory (DFT) explains as a restructuring following lattice oxygen reverse spillover.