We measure time-dependent pure-rotational coherent anti-Stokes Raman spectroscopy (CARS) spectra for room-temperature ${\mathrm{N}}_2$ , ${\mathrm{O}}_2$ , ${\mathrm{CO}}_2$ , ${\mathrm{C}}_2{\mathrm{H}}_4$ , and ${\mathrm{C}}_3{\mathrm{H}}_8$ , as well as in a ${\mathrm{C}}_3{\mathrm{H}}_8$ diffusion flame, using picosecond lasers. Because Raman coherences for ${\mathrm{N}}_2$ and ${\mathrm{O}}_2$ persist significantly longer than those for the other species, delayed probing can significantly reduce unwanted resonant contributions to rotational coherent anti-Stokes Raman spectroscopy spectra, enabling temperature and relative ${\mathrm{O}}_2/{\mathrm{N}}_2$ concentration determination in fuel-rich gas mixtures. Delayed probing also eliminates interference from smeared vibrational CARS. Probe delay affects both the temperature and relative ${\mathrm{O}}_2/{\mathrm{N}}_2$ concentrations inferred from rotational spectra when using a standard frequency-domain analysis.