<p>Single-shot terahertz (THz) spectroscopy probes sub-picosecond, non-repetitive events by combining the advantages of laser absorption with phase-sensitive interferometry. However, its usage as a quantitative tool is hindered by the chirp penalty of the spectral encoding scheme, where a narrow probe bandwidth distorts THz signals, limiting the bandwidth and spectral resolution of THz measurements. In this work, we introduce Supercontinuum-Enhanced Terahertz Spectroscopy (SETS), a method that leverages a broadband supercontinuum probe to overcome these challenges. SETS is shown to increase the usable bandwidth from 1.5 to 2.3 THz (based on the chirped pulse width and supercontinuum bandwidth), reduce signal distortion by 50%, and mitigate null frequencies. Experiments on argon plasma and water vapor, supported by modeling, show SETS enables simultaneous measurement of electron density, collision frequency, and absorption spectra. By mitigating core limitations of single-shot diagnostics, SETS offers a scalable path for quantitative, high-resolution measurements in dynamic, reactive media.</p>