Grapevine rootstocks may supply water to the scion according to the transpiration demand, thus modulating plant responses to water deficit, but the scion variety can alter these responses, as well. The rootstock genotypes' effect on the scion physiological response, aquaporin expression, and hormone concentrations in the xylem and the leaf was assessed under well watered (WW) and water stress (WS) conditions. Under WW, vines grafted onto 1103P and R110 rootstocks (the more vigorous and drought-tolerant) showed higher photosynthesis (A), stomatal conductance (g), and hydraulic conductance (Kh) compared with the less vigorous and drought-sensitive rootstock (161-49C), while under WS, there were hardly any differences between vines depending on the rootstock grafted. Besides, stomatal traits were affected by drought, which was related to g, but not by the rootstock. Under WS conditions, all and aquaporins were up-regulated in the vines grafted onto 1103P and down-regulated in the ones grafted onto 161-49C. The 1103P capability to tolerate drought was enhanced by the up-regulation of all and aquaporins, lower ABA synthesis, and higher ACC/ABA ratios in leaves during WS compared with 161-49C. It was concluded that, under WW conditions, transpiration and stomatal control were rootstock-dependent. However, under WS conditions, alterations in the molecular components of water transport and hormone concentration of the scion resulted in similar gas exchange values in the studied scions grafted onto different rootstocks.