We consider a d-dimensional stochastic lattice gas of interacting particles, diffusing under the influence of a short-ranged, attractive Ising Hamiltonian and a ‘‘hybrid’’ external field which is a superposition of a uniform and an annealed random drive, acting in orthogonal subspaces of dimensions one and m, respectively. Driven into a nonequilibrium steady state, the half-filled system phase segregates via a continuous transition at a field-dependent critical temperature. Using renormalization-group techniques, we show that its critical behavior falls into a new universality class with upper critical dimension dc=5-m, characterized by two distinct anisotropy exponents, which, like all other indices, are computed exactly to all orders in perturbation theory.