In this Letter, we report on sub-millisecond response time mid-infrared dual-comb spectroscopy using a balanced asymmetric (dispersive) dual-comb setup with a matched pair of plasmon-enhanced-waveguide dispersion-compensated quantum cascade lasers. The system performance is demonstrated by measuring spectra of Bromomethane (CH3Br) and Freon 134a (CH2FCF3) at approximately 7.8 μm. A purely computational phase and timing-correction procedure is used to validate the coherence of the quantum cascade lasers frequency combs and to enable coherent averaging over the time scales investigated. The system achieves a noise-equivalent absorption better than 1×10−3  Hz−1/2, with a resolution of 9.8 GHz (0.326  cm−1) and an optical bandwidth of 1 THz (32  cm−1), with an average optical power of more than 1 mW per spectral element.