A sensitive voltammetric sensor based on palladium nanoparticles (PdNPs) and poly-bromocresol green (pBG) composite layer immobilized on amide functionalized single-walled carbon nanotubes (AmSWCNTs) modified pyrolytic graphite (PdNPs:pBG/AmSWCNTs/PG) has been prepared for the simultaneous determination of adenosine triphosphate (ATP) catabolites, inosine (INO), hypoxanthine (HX), xanthine (XT), and uric acid (UA). The modified PdNPs:pBG/AmSWCNTs/PG was characterized by electrochemical experiments and surface analysis, which exhibited exceptional electrocatalytic effects towards the oxidation of INO, HX, XT, and UA with a significant enhanced peak current and well resolved peaks separation for all the analytes. The linear calibration curves were obtained in the concentration range of 0.001–175 µM, 0.001–200 µM, 0.001–150 µM, and 0.001–200 µM and limits of detection were found as 0.95 nM, 1.04 nM, 1.07 nM, and 0.43 nM corresponding to INO, HX, XT, and UA, respectively. The common metabolites present in the biological fluids did not interfere in the determination. The applicability of the proposed sensor was successfully demonstrated by determining INO, HX, XT, and UA in the human plasma and urine and the obtained results were validated by using HPLC.