Bringing two miscible fluids into contact naturally generates strong gradients in surface tension. Here, we investigate such a Marangoni-driven flow by continuously supplying isopropyl alcohol (IPA) on a film of water, using micron-sized droplets of IPA-water mixtures. These droplets create a localized depression in surface tension that leads to the opening of a circular, thin region in the water film. At the edge of the thin region, there is a growing rim that collects the water of the film, reminiscent of Marangoni spreading due to locally deposited surfactants. In contrast to the surfactant case, the driving by IPA-water drops gives rise to a dynamics of the thin zone that is independent of the initial layer thickness. The radius grows as r ~ t1/2, which can be explained from a balance between Marangoni and viscous stresses. We derive a scaling law that accurately predicts the influence of the IPA flux as well as the thickness of the thin film at the interior of the spreading front.