The weak lithosphere of the Tibetan plateau is surrounded by rigid crustal blocks and the transition between these regimes plays a key role in the ongoing collision between India and Eurasia. Geophysical data and magmatic evidence support the notion that partial melt exists within the anomalously hot crust of northern Tibet. The Kunlun Fault, which accommodates the plateau's eastward extrusion, has been identified as a significant rheological boundary between weak, warm Tibetan crust and the rigid eastern Kunlun-Qaidam block. Here we present reanalyses and remodelling of existing magnetotelluric data, using an anisotropy code to obtain revised resistivity models. We find unequivocal evidence for anisotropy in conductivity at the northern edge of the Tibetan plateau. We interpret this anisotropy as the signature of intrusion of melt that penetrates north from the Tibetan plateau and weakens the crust beneath the Kunlun Shan. We suggest that our identification of a melt intrusion at the northern edge of the Tibetan plateau compromises the previous identification of the Kunlun Fault as an important rheological boundary. We conclude that the crustal melt penetration probably characterizes the growth of the plateau to the north, as well as accommodating the north-south crustal shortening in Tibet.