During the Paleozoic, sedimentary basins developed within Gondwana without evolving to diverging plate boundaries. Such intracontinental basins present long subsidence histories with multiple phases of accelerated subsidence that are not always easily explained by far-field tectonic forces, and may be driven by processes other than rifting and thermal subsidence. Here we investigate the subsidence of Paleozoic Australian intracontinental basins by comparing one-dimensional backstripped tectonic subsidence histories from the western Australian Canning and Southern Carnarvon Basins and the central Australian Cooper Basin to forward subsidence models for pure shear lithospheric thinning. We make the hypothesis that differences between observed and model subsidence may be explained by mantle-flow driven topography, in addition to tectonic forces. To test this hypothesis, we compute dynamic topography from the first geodynamic models of mantle flow spanning the entire Phanerozoic Eon, and we analyse the relationship between dynamic topography and anomalous basin subsidence to dynamic topography and mantle flow. Although reconstructions of mantle flow in deep geological times are uncertain, our results suggest that long-wavelength dynamic topography could explain aspects of the complex tectonic histories intracontinental basins. In the presented reconstruction of mantle flow, topographic rebound following the sinking of a Cambrian aged slab resulted in a minor phase of dynamic uplift in the Cooper Basin in middle Permian times. Throughout Carboniferous-Triassic times Australia was positioned above a mantle upwelling driven by a hot structure at the base of the mantle. Structural uplift in the Canning and Southern Carnarvon basins during the Triassic-Jurassic interval was augmented by dynamic uplift produced by that large-scale upwelling, and possibly augmented by a focused active mantle plume during the Permo-Triassic. In Late Jurassic-Cretaceous times, Australia drifted east away from the mantle upwelling, resulting in a period of subsidence in the Canning and Southern Carnarvon basins. During the Cretaceous the Cooper Basin moved over a downwelling produced by long-lived subduction along the east Australian margin, resulting in a period of accelerated subsidence.