A considerable amount of research has focused on how and when the Tibetan plateau formed in the wake of tectonic convergence between India and Asia. Although far less enquiry has addressed the controls on river incision into the plateau itself, widely accepted theory predicts that steep fluvial knick points (river reaches with very steep gradients) in the eastern Himalayan syntaxis at the southeastern plateau margin should erode rapidly, driving a wave of incision back into the plateau. Preservation of the plateau edge thus presents something of a conundrum that may be resolved by invoking either differential rock uplift matching erosional decay, or other mechanisms for retarding bedrock river incision in this region where high stream power excludes the potential for aridity as a simple limit to dissection of the plateau. Here we report morphologic evidence showing that Quaternary depression of the regional equilibrium line altitude, where long-term glacier mass gain equals mass loss, was sufficient to repeatedly form moraine dams on major rivers: such damming substantially impeded river incision into the southeastern edge of the Tibetan plateau through the coupled effects of upstream impoundment and interglacial aggradation. Such glacial stabilization of the resulting highly focused river incision centred on the Tsangpo gorge could further contribute to initiating and accentuating a locus of rapid exhumation, known as tectonic anaeurysm.