We calculate the next-to-leading order fully unintegrated hard scattering coefficient for unpolarized gluon-induced deep inelastic scattering using the logical framework of parton correlation functions developed in previous work. In our approach, exact four-momentum conservation is maintained throughout the calculation. Hence, all nonperturbative functions, like parton distribution functions, depend on all components of parton four-momentum. In contrast to the usual collinear factorization approach where the hard scattering coefficient involves generalized functions (such as Dirac δ functions), the fully unintegrated hard scattering coefficient is an ordinary function. Gluon-induced deep inelastic scattering provides a simple illustration of the application of the fully unintegrated factorization formalism with a nontrivial hard scattering coefficient, applied to a phenomenologically interesting case. Furthermore, the gluon-induced process allows for a parametrization of the fully unintegrated gluon distribution function. © 2008 The American Physical Society.