We present a new method to standardize Type Ia supernova (SN Ia) luminosities to ~<0.13mag using flux ratios from a single flux-calibrated spectrum per SN. Using Nearby Supernova Factory spectrophotometry of 58 SNe Ia, we performed an unbiased search for flux ratios that correlate with SN Ia luminosity. After developing the method and selecting the best ratios from a training sample, we verified the results on a separate validation sample and with data from the literature. We identified multiple flux ratios whose correlations with luminosity are stronger than those of light curve shape and color, previously identified spectral feature ratios, or equivalent width measurements. In particular, the flux ratio R(642/443)=Flux(642nm)/Flux(443nm) has a correlation of 0.95 with SN Ia absolute magnitudes. Using this single ratio as a correction factor produces a Hubble diagram with a residual scatter standard deviation of 0.125+/-0.011mag, compared with 0.161+/-0.015mag when fit with the SALT2 light curve shape and color parameters x1 and c. The ratio R(642/443) is an effective correction factor for both extrinsic dust reddening and intrinsic variations such as those of SN 1991T-like and SN 1999aa-like SNe. When combined with broad-band color measurements, spectral flux ratios can standardize SN Ia magnitudes to ~0.12mag. These are the first spectral metrics that give robust improvements over the standard normalization methods based upon light curve shape and color, and they provide among the lowest scatter Hubble diagrams ever published.