Despite the importance of precipitation and moisture transport over the Tibetan Plateau for glacier mass balance, river runoff and local ecology, changes in these quantities remain highly uncertain and poorly understood. Here we use observational data and model simulations to explore the close relationship between summer rainfall variability over the southwestern Tibetan Plateau (SWTP) and that over central-eastern India (CEI), which exists despite the separation of these two regions by the Himalayas. We show that this relationship is maintained primarily by 'up-and-over' moisture transport, in which hydrometeors and moisture are lifted by convective storms over CEI and the Himalayan foothills and then swept over the SWTP by the mid-tropospheric circulation, rather than by upslope flow over the Himalayas. Sensitivity simulations confirm the importance of up-and-over transport at event scales, and an objective storm classification indicates that this pathway accounts for approximately half of total summer rainfall over the SWTP.