We present fundamental parameters for 110 canonical K- and M-type (1.3-0.13M_{sun}_) Taurus-Auriga young stellar objects (YSOs). The analysis produces a simultaneous determination of effective temperature (Teff), surface gravity (logg), magnetic-field strength (B), and projected rotational velocity (vsini). Our method employed synthetic spectra and high-resolution (R~45000) near-infrared spectra taken with the Immersion GRating INfrared Spectrometer (IGRINS) to fit specific K-band spectral regions most sensitive to those parameters. The use of these high-resolution spectra reduces the influence of distance uncertainties, reddening, and non-photospheric continuum emission on the parameter determinations. The median total (fit+systematic) uncertainties were 170K, 0.28dex, 0.60kG, 2.5km/s for Teff, logg, B, and vsini, respectively. We determined B for 41 Taurus YSOs (upper limits for the remainder) and find systematic offsets (lower Teff, higher logg and vsini) in parameters when B is measurable but not considered in the fit. The average logg for the Class II and Class III objects differs by 0.23+/-0.05dex, which is consistent with Class III objects being the more evolved members of the star-forming region. However, the dispersion in logg is greater than the uncertainties, which highlights how the YSO classification correlates with age (logg), yet there are exceptionally young (lower logg) Class III YSOs and relatively old (higher logg) Class II YSOs with unexplained evolutionary histories. The spectra from this work are provided in an online repository along with TW Hydrae Association comparison objects and the model grid used in our analysis.