During their asymptotic giant branch evolution, low-mass stars lose a significant fraction of their mass through an intense wind, enriching the interstellar medium with products of nucleosynthesis. We observed the nearby oxygen-rich asymptotic giant branch star IK Tau using the high-resolution HIFI spectrometer onboard Herschel. We report on the first detection of (H2O)-O-16 and the rarer isotopologues (H2O)-O-17 and (H2O)-O-18 in both the ortho and para states. We deduce a total water content (relative to molecular hydrogen) of 6.6 x 10(-5), and an ortho-to-para ratio of 3:1. These results are consistent with the formation of H2O in thermodynamical chemical equilibrium at photospheric temperatures, and does not require pulsationally induced non-equilibrium chemistry, vaporization of icy bodies or grain surface reactions. High-excitation lines of (CO)-C-12, (CO)-C-13, (SiO)-Si-28, (SiO)-Si-29, (SiO)-Si-30, HCN, and SO have also been detected. From the observed line widths, the acceleration region in the inner wind zone can be characterized, and we show that the wind acceleration is slower than hitherto anticipated.