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A simple, eco-friendly four analytical methods were established by improving the selectivity through the application of mathematical processing of UV absorption spectra for concurrent quantification of chlorthalidone (CTL) and azelnidipine (AZE). The UV absorption spectra were recorded using environment-friendly ethanol (10% v/v) and were mathematically processed using simple software provided with a UV spectrophotometer. The analytes’ peak amplitude was determined using zero-crossing point first derivative spectra and ratio first derivative spectra of CTL and AZE, which were measured at 238.5 nm and 239.5 nm for CTL and 272.1 nm and 342.1 nm for AZE, respectively. The peak amplitude difference was determined from the ratio spectra of CTL and AZE by measuring the peak amplitudes at 211.8 and 267.2 nm for CTL and 328.4 and 286.1 nm for AZE. Further, ratio spectra of CTL and AZE were converted into zero-order spectra by subtracting the constant followed by multiplication with divisor spectra, and the peak amplitudes were measured at 226.9 nm and 257.3 nm for CTL and AZE zero-order spectra, respectively. Further, validation results of all the four methods confirmed the accuracy and precision of the methods by displaying good recovery (98.37–100.34%) and percentage relative standard deviation (0.397–1.758%), respectively. Good linearity was observed in the range of 1–15 μg/mL for both analytes with less than a 1 μg/mL limit of quantification. Further, the greenness and whiteness of the methods were evaluated by recently proposed AGREEness, complexGAPI, and white analytical chemistry techniques. The proposed UV spectroscopic methods were environmentally friendly, safe, economic, and effective, hence, could be used for regular quality control study of a formulation containing CTL and AZE.