Integral cross-section measurements for the system water-H-2 in molecular-beam scattering experiments are reported. Their analysis demonstrates that the average attractive component of the water-H-2 intermolecular potential in the well region is about 30% stronger than dispersion and induction forces would imply. An extensive and detailed theoretical analysis of the electron charge displacement accompanying the interaction, over several crucial sections of the potential energy surface (PES), shows that water-H-2 interaction is accompanied by charge transfer (CT) and that the observed stabilization energy correlates quantitatively with CT magnitude at all distances. Based on the experimentally determined potential and the calculated CT, a general theoretical model is devised which reproduces very accurately PES sections obtained at the CCSD(T) level with large basis sets. The energy stabilization associated with CT is calculated to be 2.5 eV per electron transferred. Thus, CT is shown to be a significant, strongly stereospecific component of the interaction, with water functioning as electron donor or acceptor in different orientations. The general relevance of these findings for water's chemistry is discussed.