Cavity-free lasing in atmospheric air has stimulated intense research toward a fundamental understanding of underlying physical mechanisms. In this Letter, we identify a new mechanism-a third-harmonic photon mediated resonant energy transfer pathway leading to population inversion in argon via an initial three-photon excitation of nitrogen molecules irradiated by intense 261 nm pulses-that enables bidirectional two-color cascaded lasing in atmospheric air. By making pump-probe measurements, we conclusively show that such cascaded lasing results from superfluorescence rather than amplified spontaneous emission. Such cascaded lasing with the capability of producing bidirectional multicolor coherent pulses opens additional possibilities for remote sensing applications.