Metal-poor, star-forming dwarf galaxies produce extreme nebular emission and likely played a major role in cosmic reionization. Yet, determining their contribution to the high-redshift ionizing photon budget is hampered by the lack of observations constraining the ionizing spectra of individual massive stars more metal-poor than the Magellanic Clouds (20%–50% Z ⊙). We present new Keck Cosmic Web Imager (KCWI) optical integral field unit spectroscopy of the only H ii region in Leo P (3% Z ⊙), which is powered by a single O star. We calculate the required production rate of photons capable of ionizing hydrogen and helium from the observed Hβ and He i λ4471 emission-line fluxes. Remarkably, we find that the ionizing photon production rate and spectral hardness predicted by a tlusty model fit to the stellar spectral energy distribution agrees with our observational measurements within the uncertainties. We then fit Cloudy photoionization models to the full suite of optical emission lines in the KCWI data and show that the shape of the same tlusty ionizing continuum simultaneously matches lines across a wide range of ionization energies. Finally, we detect O iii] and N iii] nebular emission in the Hubble Space Telescope far-ultraviolet spectrum of the Leo P H ii region, and highlight that the rarely observed N iii] emission cannot be explained by our Cloudy models. These results provide the first observational evidence that widely used, yet purely theoretical, model spectra accurately predict the ionizing photon production rate from late-O stars at very low metallicity, validating their use to model metal-poor galaxies both locally and at high redshift.