New molecular beam scattering experiments are reported for the water-hydrogen system. Integral cross sections of the first rotational excitations of para- and ortho-H2O by inelastic collisions with normal-H2 were determined by crossing a beam of H2O seeded in He with a beam of H2. H2O and H2 were cooled in the supersonic expansion down to their lowest rotational levels. Crossed-beam scattering experiments were performed at collision energies from 15 cm-1 (below the threshold for the excitation to the lowest excited rotational state of H2O: 18.6 cm-1) up to 105 cm-1 by varying the beam crossing angle. The measured state-to-state cross-sections were compared to the theoretical cross-sections (close-coupling quantum scattering calculations): the good agreement found further validates both the employed potential energy surface describing the H2O-H2 van der Waals interaction and the state-to-state rate coefficients calculated with this potential in the very low temperature range needed for the modeling of interstellar media.