Models of how high elevations formed across Tibet predict: (a) the continuous thickening of a "viscous sheet"; (b) time-dependent, oblique stepwise growth; and (c) synchronous deformation across Tibet that accompanied collision. Our new observations may shed light on this issue. Here, we use 40Ar/39Ar and (U-Th)/He thermochronology from massifs in the hanging walls of thrust structures along the Kunlun Belt, the first-order orogenic range at the northern Tibetan margin, to elucidate the exhumation history. The results show that these massifs, and hence the plateau margin, were subject to slow, steady exhumation during the Early Cenozoic, followed by a pulse of accelerated exhumation during 40-35 Ma. The exhumation rate increases westward (from ~0.22 to 0.34 and 0.5 mm/yr). The two-fold increase in exhumation in the western part (0.5 mm/yr) compared to the eastern part suggests westward increases in exhumation and compressional stress along the Kunlun Belt. We relate these observations to the mechanisms responsible for the oblique stepwise rise of Tibet. After collision, oblique subduction beneath Kunlun caused stronger compressional deformation in the western part than in the eastern part, resulting in differential growth and lateral extrusion.