The old, solar metallicity open cluster Messier 67 has long been considered a lynchpin in the study and understanding of the structure and evolution of solar-type stars. The same is arguably true for stellar remnants - the white dwarf population of M67 provides crucial observational data for understanding and interpreting white dwarf populations and evolution. In this work, we determine the white dwarf masses and derive their progenitor star masses using high signal-to-noise spectroscopy of warm ($gtrsim10,000$ K) DA white dwarfs in the cluster. From this we are able to derive each white dwarfs position on the initial-final mass relation, with an average $M_{mathrm WD} = 0.60pm 0.01 M_{odot}$ and progenitor mass $M_i = 1.52pm 0.04 M_{odot}$. These values are fully consistent with recently published linear and piecewise linear fits to the semi-empirical initial-final mass relation and provide a crucial, precise anchor point for the initial-final mass relation for solar-metallicity, low-mass stars. The mean mass of M67 white dwarfs is also consistent with the sharp narrow peak in the local field white dwarf mass distribution, indicating that a majority of recently-formed field white dwarfs come from stars with progenitor masses of $approx 1.5 M_{odot}$. Our results enable more precise modeling of the Galactic star formation rate encoded in the field WD mass distribution.
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