Cadmium (Cd) and lead (Pb) are classified as category one toxicants. The provisional guideline values, according to the World Health Organization (WHO), for Cd and Pb are 3 and 10 ppb, respectively. An easy, quick, and cheap analytical technique is in demand for the determination of these toxic heavy metals in water. Hence, a novel electrochemical sensing platform is developed by modifying the glassy carbon electrode with ethylenediaminetetraacetic acid (EDTA)-functionalized reduced graphene oxide (ErGO) for the low-cost simultaneous quantitation of toxic heavy-metal ions, lead and cadmium, in real water samples. EDTA is grafted to the surface of graphene oxide, via amine linkage, and the oxygen functionality is reduced by a green agent, tyrosine. Various physical and electrochemical characterizations of the as-prepared electrocatalytic material were performed by X-ray diffraction (XRD), Fourier transform infrared (FTIR) spectroscopy, thermogravimetric analysis (TGA), ζ-potential, ultraviolet diffuse reflectance spectroscopy (UV-DRS), cyclic voltammetry (CV), electrochemical impedance spectroscopy (EIS), etc. The glassy carbon electrode (GCE) is modified with ErGO by a simple drop-casting method for simultaneous metal-ion quantitation by differential pulse voltammetry (DPV). EDTA functionalization of graphene oxide and its further reduction using the green agent enhance the stability and sensitivity of the electrode substrate. The limits of detection for cadmium and lead ions calculated for ErGO/GCE are 1.02 and 2.52 ppb, while the limits of quantification for lead and cadmium ions are 3.41 and 8.4 ppb, and their sensitivities are 0.8 and 0.6 nA/ppb, respectively. Real river water contains 200.2 ± 0.38 ppb of Pb2+ ions (mean ± stdev, n = 3) by the DPV technique, which is validated by ICP-OES analysis.