An oven appliance having an oven chamber positioned within a cabinet and a top panel defining one or more vent apertures includes a false back assembly for facilitating the containment of spilled fluids and the cooling of electronic components within the cabinet. The false back assembly includes a false back spaced apart from a range back to define a spill channel. A spill deflector is positioned below the vent apertures and above the spill channel along the vertical direction such that the spill deflector is configured for collecting fluids spilled through the vent apertures and directing the spilled fluids to the spill channel where they may be safely routed around sensitive electronic components.