We describe the analytic continuation of two-loop four-point functions with one off-shell external leg and internal massless propagators from the Euclidean region of space-like decay to Minkowskian regions relevant to all and reactions with one space-like or time-like off-shell external leg. Our results can be used to derive two-loop master integrals and unrenormalized matrix elements for hadronic vector-boson-plus-jet production and deep inelastic two-plus-one-jet production, from results previously obtained for three-jet production in electron--positron annihilation.