Rotationally resolved, broadband absorption spectra of the fundamental vibrational transition of the asymmetric C-H stretch mode of methane are measured under single-laser-shot conditions using time-resolved optically gated absorption (TOGA). The TOGA approach exploits the difference in timescales between a broadband, fs-duration excitation source and the ps-duration absorption features induced by molecular absorption to allow effective suppression of the broadband background spectrum, thereby allowing for sensitive detection of multi-transition molecular spectra. This work extends the TOGA approach into the mid-infrared (mid-IR) spectral regime, allowing access to fundamental vibrational transitions while providing broadband access to multiple mid-IR transitions spanning ∼150 cm-1 (∼160 nm) near 3.3 μm, thereby highlighting the robustness of this technique beyond previously demonstrated electronic spectroscopy. Measurements are conducted in a heated gas cell to determine the accuracy of the simultaneous temperature and species-concentration measurements afforded by this single-shot approach in a well-characterized environment. Application of this approach toward fuel-rich methane-nitrogen-oxygen flames is also demonstrated.