Diabetes mellitus and concurrent hypertension disorder are dreadful all over the world and are often managed by some drugs, such as metformin hydrochloride (MFH), enalapril maleate (ENM), and captopril (CAP). In this work, a reliable and fast quantitative analysis of these three components in tablets was carried out by Tchebichef image moment method and multivariate curve resolution with alternating least squares on three-dimensional (3D) spectra obtained by high-performance liquid chromatography coupled with photodiode array detection (HPLC-PAD). 3D spectra were obtained within only 2 min, and linear quantitative models were established by stepwise regression based on the calculated image moments. Among these two methods, Tchebichef image moment method showed outcome distinction. The correlation coefficients of cross-validation (RLoo-cv) are more than 0.988, while their recoveries are 100.1 ± 1.7% (MFH), 95.4 ± 5.4% (ENM), and 105.3 ± 5.7% (CAP), respectively. The intra- and inter-day precisions (RSD) are less than 5.42%. The proposed methods were also applied to the analysis of real tablets. This study reveals the effectiveness and convenience of the proposed image-moment method that may be a potential technology for the quality control and investigation of drugs in routine analysis.