In this work, we present detailed constraints on the metallicity dependence of the high-mass X-ray binary (HMXB) X-ray luminosity function (XLF). We analyze ~5Ms of Chandra data for 55 actively star-forming galaxies at D<=30Mpc, with gas-phase metallicities spanning 12+log(O/H)~7-9.2. Within the galactic footprints, our sample contains a total of 1311 X-ray point sources, of which ~49% are expected to be HMXBs, with the remaining sources likely to be low-mass X-ray binaries (LMXBs; ~22%) and unrelated background sources (~29%). We construct a model that successfully characterizes the average HMXB XLF over the full metallicity range. We demonstrate that the SFR- normalized HMXB XLF shows clear trends with metallicity, showing steadily increasing numbers of luminous and ultraluminous X-ray sources (logL(erg/s)=38-40.5) with declining metallicity. However, we find that the low-luminosity (logL(erg/s)=36-38) HMXB XLF appears to show a nearly constant SFR scaling and slope with metallicity. Our model provides a revised scaling relation of integrated LX/SFR versus 12+log(O/H), and a new characterization of its SFR-dependent stochastic scatter. The general trend of this relation is broadly consistent with past studies based on integrated galaxy emission; however, our model suggests that this relation is driven primarily by the high-luminosity end of the HMXB XLF. Our results have implications for binary population synthesis models, the nature of super-Eddington accreting objects (e.g., ultraluminous X-ray sources), recent efforts to identify active galactic nucleus candidates in dwarf galaxies, and the X-ray radiation fields in the early universe during the epoch of cosmic heating at z>=10.