  We calculate the total and partial inclusive Higgs widths at leading order in
the Standard Model Effective Field Theory (SMEFT). We report results
incorporating SMEFT corrections for two and four body Higgs decays through
vector currents in this limit. The narrow width approximation is avoided and
all phase space integrals are directly evaluated. We explain why the narrow
width approximation fails more significantly in the SMEFT compared to the SM,
despite the narrowness of the observed $\rm SU(2) \times U(1)$ bosons in both
theories. Our results are presented in a manner that allows various input
parameter schemes to be used, and they allow the inclusive branching ratios and
decay widths of the Higgs to be numerically determined without a Monte Carlo
generation of phase space for each Wilson coefficient value chosen.
