We observe that the growth rate of Ga_{2}O_{3} in plasma-assisted molecular beam epitaxy can be drastically enhanced by an additional In supply. This enhancement is shown to result from a catalytic effect, namely, the rapid formation of In_{2}O_{3}, immediately followed by a transformation of In_{2}O_{3} to Ga_{2}O_{3} due to an In-Ga interatomic exchange. We derive a simple model that quantitatively describes this process as well as its consequences on the formation rate of Ga_{2}O_{3}. Moreover, we demonstrate that the catalytic action of In_{2}O_{3} allows the synthesis of the metastable hexagonal phase of Ga_{2}O_{3}. Since the Ga_{2}O_{3}(0001)/In_{2}O_{3}(111) interface is closely lattice matched, this novel growth mode opens a new path for the fabrication of sesquioxide heterostructures.