Intriguing quantum effects that result from entangled molecular rovibrational states are shown to provide a novel means for controlling both differential and total collision cross sections in identical particle diatom-diatom scattering. Computational results on elastic and inelastic scattering of para-H-2 and para-H-2 are presented, with the collision energy ranging from 400 cm(-1) to the ultracold regime. The experimental realization and possible extension to other systems are discussed. (C) 2003 American Institute of Physics.