The ability to perform detailed chemical analysis of Sun-like F-, G-, and K-type stars is a powerful tool with many applications, including studying the chemical evolution of the Galaxy and constraining planet formation theories. Unfortunately, complications in modeling cooler stellar atmospheres hinders similar analyses of M dwarf stars. Empirically calibrated methods to measure M dwarf metallicity from moderate-resolution spectra are currently limited to measuring overall metallicity and rely on astrophysical abundance correlations in stellar populations. We present a new, empirical calibration of synthetic M dwarf spectra that can be used to infer effective temperature, Fe abundance, and Ti abundance. We obtained high-resolution (R ∼ 25,000), Y-band (∼1 μm) spectra of 29 M dwarfs with NIRSPEC on Keck II. Using the PHOENIX stellar atmosphere modeling code (version 15.5), we generated a grid of synthetic spectra covering a range of temperatures, metallicities, and alpha-enhancements. From our observed and synthetic spectra, we measured the equivalent widths of multiple Fe I and Ti I lines and a temperature-sensitive index based on the FeH band head. We used abundances measured from widely separated solar-type companions to empirically calibrate transformations to the observed indices and equivalent widths that force agreement with the models. Our calibration achieves precisions in T _eff, [Fe/H], and [Ti/Fe] of 60 K, 0.1 dex, and 0.05 dex, respectively, and is calibrated for 3200 K < T _eff < 4100 K, -0.7 < [Fe/H] < +0.3, and -0.05 < [Ti/Fe] < +0.3. This work is a step toward detailed chemical analysis of M dwarfs at a precision similar to what has been achieved for FGK stars.