Nonlinear laser wave mixing is a versatile spectroscopic method for trace elemental analysis at high spectral resolution. Sub-Doppler spectral resolution allows isotope and hyperfine structure measurements of some of the elements even when using a room-pressure analytical flame (i.e., sub-Doppler but Lorentzian broadened spectra). A non-planar wave-mixing optical setup offers some advantages as compared to the conventional planar wave-mixing setup including better signal collection efficiency and easier optical alignment. Using our absorption-based wave mixing, a detection limit of 0.05 ng/mL (i.e., 50 parts-per-trillion) is reported for Rb in an air/acetylene flame, while still maintaining sub-Doppler spectral resolution for the infrared 780.0-nm Rb transition line.