The Cenozoic evolution of the Himalaya-Tibet Plateau, dictated by the India-Asia convergence, remains a subject of substantial ambiguity. Here, a thermo-mechanical model is used to show the critical controls of decelerating convergence on the formation and stabilization of distinctive tectonic structures during prolonged collision. At high constant convergence rates, similar to the late Paleogene India-Asia motions, the lower plate crust is injected beneath the overriding crust, uplifting a plateau, first, then is exhumed towards the orogeny front. Conversely, low constant convergence rates, similar to the Neogene India-Asia motions, induce crustal thickening and plateau formation without underplating or exhumation of incoming crust. Strikingly, models simulating the decelerating India-Asia convergence history portray a dynamic evolution, highlighting the transitory nature of features under decreasing convergence, as the orogen shifts to a new equilibrium. In the transitional phase, the slowing of convergence decreases basal shearing and compression, leading to extension and heating in the orogen interiors. This allows diapiric ascent of buried crust and plateau collapse, as accretion migrates to a frontal fold-and-thrust belt. The models provide insights into the multi-stage evolution of the long-lived Himalayan-Tibetan orogeny, from fast early growth of the Tibetan Plateau, through its transient destabilisation and late-stage internal extension, behind the expanding Himalayan belt.