Inverted liquid films are inherently unstable: gravity amplifies perturbations through the Rayleigh-Taylor instability (RTI), causing rupture and dripping. We show that selective evaporation in volatile binary mixtures can suppress, delay, or transform this instability by inducing solutal Marangoni stresses. Systematic experiments and a complementary theoretical model reveal three instability regimes- promotion, suppression, and sustained oscillations-set by volatility, viscosity, and surfacetension contrast. High-resolution deflectometry tracks spatiotemporal film evolution, while linear stability analysis captures the competition among gravity, capillarity, and Marangoni forces. Measurements and theoretical predictions agree well quantitatively, confirming the mechanism and establishing evaporation-driven Marangoni flow as a robust interfacial control strategy for inverted films. Our results deliver the first systematic experimental validation of solutal-Marangoni suppression of RTI in inverted configurations and provide a general framework for instability control in volatile thin films, with implications for materials processing, coating, and soft-matter hydrodynamics.