Time-resolved near-infrared absorption spectroscopy of single non-repeatable transient events is performed at high spectral resolution with a dual-comb interferometer using a continuous-wave laser followed by a single electro-optic amplitude modulator. By sharing high-speed electrical/optical components, our spectrometer greatly simplifies the implementation of dual-comb spectroscopy and offers a high mutual coherence time, measured up to 50 s, without any active stabilization system and/or data processing. The time resolution is as short as 100 µs in our experimental demonstration. For a span of 36 GHz, the mean signal-to-noise ratio of 80, at 100-MHz spectral resolution and 100-µs measurement time, enables precise determination of the parameters of rovibrational lines, including intensity or concentration.