According to the World Health Organization (WHO), an estimated 10% of pharmaceutical products distributed in developing countries are counterfeit or of substandard quality. A crucial strategy to help overcome this problem is to develop simple and easily applicable analytical methods for quality control testing of drugs, especially those administered in combinations due to their complex nature. Here, we worked towards this goal through the development of a simple, and rapid method based on High Performance Liquid Chromatography coupled with Ultraviolet detection (HPLC-UV) for the simultaneous determination of an anti-depressant free-drug combination consisting of brexpiprazole (BREX) and fluoxetine (FLX) in the presence of fluoxetine related impurities (FLX-A). Chromatographic separation was carried out employing a mixture of 45% ethanol and 55% aqueous solvent consisting of 0.1% triethylamine, 0.15 M sodium dodecyl sulfate and 0.057 M sodium dihydrogen phosphate adjusted to pH 6 using orthophosphoric acid. Separation was performed using a hypersil BDS C18 column at 50 °C, employing isocratic elution; the flow rate was set at 1.5 mL min−1 , and UV detection was performed at 220 nm. The results of the developed method reflect excellent analytical performance. Linearity was observed over a concentration range of 5–80 mg mL−1 for both drugs with correlation coefficients of 0.9996 and 0.9998 for BREX and FLX, respectively. The respective LOQ and LOD values were found to be 2.70 and 4.41 mg mL—1 and 0.83 and 1.46 mg mL−1 for BREX and FLX; in addition, the developed method was utilized to test the purity of both drugs in pharmaceutical formulations by monitoring fluoxetine-related impurities. The developed method was also determined to be eco-friendly, as testing with four available assessment tools demonstrated its superior greenness, especially represented by an AGREE score of 0.83.