The Carboniferous-Permian transition (CPT) was Earth's last pre-Quaternary icehouse-greenhouse transition, recording major shifts in late Palaeozoic climate regimes and increased continental seasonality over approximately 40 Myr. Its parallels to Quaternary climate change have inspired recent investigations into the impacts of purported rainforest collapse on palaeotropical vertebrate diversity, but little is known about how the protracted spatial dynamics of this transition impacted the emergence of modern tetrapod lineages. Here, we apply ecological ordinance analyses on a dataset of 286 CPT fossil vertebrate localities binned across four physiographic regions forming a palaeoequatorial transect. Our results clarify the spatiotemporal expansion of land-living vertebrates, demonstrating that the reduction of tropical wetlands accommodated emerging dryland-adapted amniote faunas from a western Pangaean epicentre. We call this west-east lag the 'Vaughn-Olson model': CPT climatic transitions were regionally diachronous with delayed proliferation of amniote-dominated dryland assemblages in the east. By combining our ecological analyses with a phylogenetic approach, we demonstrate that this pattern also applies to some co-occurring total-group amphibians, suggesting that there was pervasive selection for such dryland adaptations across the crown tetrapod tree, in contrast with stem tetrapods and 'fishes'.