We present here the first full computation of the rovibrational quenching of a polyatomic molecule (water) by a rotating molecular projectile (H2). The computation is performed for quenching from the first bending mode of water at ν ≃ 1595 cm-1 with a rotation energy of up to ∼400 cm-1 in the bending mode. Molecular hydrogen is in its para and ortho modifications; it is rotating with a rotational quantum number of up to 4 and 3, respectively. All computations are performed on a very reliable and fully tested potential water-hydrogen energy surface of full dimensionality. Dynamics is performed in the full coupled channel formalism in the rigid bender approximation with a decoupling of the water rotation and vibration bases. Rate coefficients are converged for a kinetic temperature range 50-500 K. The crucial importance of the proper treatment of the projectile rotation is emphasized with orders of magnitude differences between the different channels for the H2 rotation. Sensitivity to the actual rovibrational initial state of water exists but in a weaker manner. Overall quenching rate coefficients are about 10-12 cm3 s-1, remaining one to three orders of magnitude lower than pure rotational quenching. They should be employed to model denser and warmer astrophysical media, such as high atmospheres or star and planet forming regions, which are to be explored by infrared space telescopes, such as JWST.