We present a model-independent calculation of hadron matrix elements for all dimension-6 operators associated with baryon number violating processes using lattice QCD. The calculation is performed with the Wilson quark action in the quenched approximation at beta = 6/g(2) = 6.0 on a 28(2) x 48 x 80 lattice. Our results cover all the matrix elements required to estimate the partial lifetimes of (proton,neutron)-->(pi,K,eta) + (<(nu)over bar>,e(+), mu(+)) decay modes. We point out the necessity of disentangling two Form factors that contribute to the matrix element; previous calculations did not make the separation, which led to an underestimate of the physical matrix elements. With a correct separation, we find that the matrix elements have values 3-5 times larger than the smallest estimates employed in phenomenological analyses of the nucleon decays, which could give strong constraints on several GUT models. We also find that the values of the matrix elements are comparable with the tree-level predictions of the chiral Lagrangian.