The topographical power spectrum of Venus provides important clues to the planet's past evolution. Venus is currently experiencing stagnant lid global tectonics, but it may may have had both an Earth-like climate as well as active (or incipient) plate tectonics for an extended interval of its history. By drawing detailed contrast with the strong low-order odd-\(\ell\) dominated global topography of Earth, we demonstrate that the relatively flat Venusian topography can be interpreted to have arisen from the transition from active terrestrial-like plate tectonics to the current stagnant lid configuration at a time \(\tau \sim 600\) Myr before present. This scenario is plausible if loss of oceans and the attendant transition to a CO2-dominated atmosphere were accompanied by rapid continental-scale erosion, followed by gradual lava resurfacing at an outflow rate, \(r\sim20\,{\rm km}^{3}\,{\rm yr}^{-1}\).