We use the statistical power of the MaNGA integral-field spectroscopic galaxy survey to improve the definition of strong line diagnostic boundaries used to classify gas ionization properties in galaxies. We detect line emission from 3.6 million spaxels distributed across 7400 individual galaxies spanning a wide range of stellar masses, star formation rates, and morphological types, and find that the gas-phase velocity dispersion sigma_HAlpha correlates strongly with traditional optical emission line ratios such as [S II]/HAlpha, [N II]/HAlpha, [O I]/HAlpha, and [O III]/HBeta. Spaxels whose line ratios are most consistent with ionization by galactic HII regions exhibit a narrow range of dynamically cold line of sight velocity distributions (LOSVDs) peaked around 25 km/s corresponding to a galactic thin disk, while those consistent with ionization by active galactic nuclei (AGN) and low-ionization emission-line regions (LI(N)ERs) have significantly broader LOSVDs extending to 200 km/s. Star-forming, AGN, and LI(N)ER regions are additionally well separated from each other in terms of their stellar velocity dispersion, stellar population age, HAlpha equivalent width, and typical radius within a given galaxy. We use our observations to revise the traditional emission line diagnostic classifications so that they reliably identify distinct dynamical samples both in two-dimensional representations of the diagnostic line ratio space and in a multi-dimensional space that accounts for the complex folding of the star forming model surface. By comparing the MaNGA observations to the SDSS single-fiber galaxy sample we note that the latter is systematically biased against young, low metallicity star-forming regions that lie outside of the 3 arcsec fiber footprint.