Despite longstanding research on the age and formation of the Tibetan Plateau, the controls on the erosional decay of its margins remain controversial. Pronounced aridity and highly localized rock uplift have traditionally been viewed as limits to the dissection of the plateau by bedrock rivers. Recently, however, glacier dynamics and landsliding have been argued to retard headward fluvial erosion into the plateau interior by forming dams and protective alluvial fill. Here, we report a conspicuous clustering of hundreds of natural dams along the Indus and the Tsangpo Rivers where these cross the Himalayan syntaxes. The Indus is riddled by hundreds of dams composed of debris from catastrophic rock avalanches, forming the largest concentration of giant landslide dams known worldwide, whereas the Tsangpo seems devoid of comparable landslide dams. In contrast, glacial dams such as river-blocking moraines in the headwaters of both rivers are limited to where isolated mountain ranges intersect the regional snowline. We find that to first-order, high local topographic relief along both rivers corresponds to conspicuously different knickzones and differences in the type and potential longevity of these dams. In both syntaxes, glacier and landslide dams act as a negative feedback in response to fluvial dissection of the plateau margins. Natural damming protects bedrock from river incision and delays headward knickpoint migration, thereby helping stabilize the southwestern and southeastern margins of the Tibetan Plateau in concert with the effects of upstream aridity and localized rock uplift.