We target the thermal emission spectrum of the non-transiting gas giant HD 88133 b with high-resolution near-infrared spectroscopy, by treating the planet and its host star as a spectroscopic binary. For sufficiently deep summed flux observations of the star and planet across multiple epochs, it is possible to resolve the signal of the hot gas giant's atmosphere compared to the brighter stellar spectrum, at a level consistent with the aggregate shot noise of the full data set. To do this, we first perform a principal component analysis to remove the contribution of the Earth's atmosphere to the observed spectra. Then, we use a cross-correlation analysis to tease out the spectra of the host star and HD 88133 b to determine its orbit and identify key sources of atmospheric opacity. In total, six epochs of Keck NIRSPEC L-band observations and three epochs of Keck NIRSPEC K-band observations of the HD 88133 system were obtained. Based on an analysis of the maximum likelihood curves calculated from the multi-epoch cross-correlation of the full data set with two atmospheric models, we report the direct detection of the emission spectrum of the non-transiting exoplanet HD 88133 b and measure a radial projection of the Keplerian orbital velocity of 40+/-15km/s, a true mass of 1.02_-0.28_^+0.61^M_J_, a nearly face-on orbital inclination of 15_-5_^+6^{deg}, and an atmosphere opacity structure at high dispersion dominated by water vapor. This, combined with 11 years of radial velocity measurements of the system, provides the most up-to-date ephemeris for HD 88133.