Spectroscopic detection of gases can be achieved by measuring a few species-specific absorption lines, requiring very accurate wavelength control. Alternatively, it can be achieved by using many wavelengths spread over a wide range; each wavelength need not be optimal spectroscopically, but all collectively form a unique fingerprint for the species of interest. Statistical regression can be used to quantify their concentrations. An experimental evaluation of this concept involved using a 3.1 microm broadly tunable Sb-based mid-IR laser to discriminate and measure mixtures of acetylene and water vapor with absorption spectral overlaps. As many as 30 wavelengths from approximately 3200 to approximately 3280 cm-1 were used to measure 5 x 5 combinations of the two-gas concentration. Statistical analysis of the results validates the concept. Each gas concentration was consistently and reliably measured without any problem of interference from the other. In addition, the method was sufficiently sensitivite to detect unusual discrepancies by use of statistical analysis. Optimization of the system's detection capability and its receiver-operating characteristics is demonstrated. The results suggest that the statistical multiwavelength broadband approach to detection of gas mixture can be a highly effective alternative to species-specific single-line spectroscopy.