We detail the effects of Cl and S functionalization on the superconducting properties of layered (bulk) and monolayer niobium carbide (Nb2C) MXene crystals, based on first-principles calculations combined with Eliashberg theory. For bulk layered Nb2CCl2, the calculated superconducting transition temperature (Tc) is in very good agreement with the recently measured value of 6 K. We show that Tc is enhanced to 10 K for monolayer Nb2CCl2, due to an increase in the density of states at the Fermi level, and the corresponding electron-phonon coupling. We further demonstrate feasible gate- and strain-induced enhancements of Tc for both bulk-layered and monolayer Nb2CCl2 crystals, resulting in Tc values of around 38 K. In the S-functionalized Nb2CCl2 crystals, our calculations reveal the importance of phonon softening in understanding their superconducting properties. Finally, we predict that Nb3C2S2 in bulk-layered and monolayer forms is also superconducting, with a Tc of around 28 K. Considering that Nb2C is not superconducting in pristine form, our findings promote functionalization as a pathway towards robust superconductivity in MXenes.