This work is the first presentation of the synthesis of few-layer graphene decorated with gold and silver nanoparticles (Gr–Au–Ag) by chemical vapor deposition over a catalytic system formed of bimetallic Au–Ag nanoclusters supported on MgO and with methane used as the source of carbon. The sheetlike morphology of the graphene nanostructures, with mean sizes in the range of hundreds of nanometers, was observed by high-resolution electron microscopy. The distinctive feature found in all the samples was the regular rectangular or square shapes. This multi-component organic–inorganic nanomaterial was used to modify a platinum substrate and subsequently employed for the detection of carbamazepine, an anti-convulsion drug. UV/Vis spectroscopy revealed that a strong hypochromism occurred over time, after mixing solutions of graphene–Au–Ag with carbamazepine. This can be attributed to π–π stacking between the aromatic groups of the two compounds. Linear sweep voltammetry (LCV) provided evidence that the modified platinum substrate presented a significant electrocatalytic reaction toward the oxidation of carbamazepine. The intensity of the current was found to increase by up to 2.5 times, and the oxidation potential shifted from +1.5 to +1.35 V(Ag/AgCl) in comparison with the unmodified electrode. Electrochemical impedance spectroscopy (EIS) was further used to thoroughly assess the activity of the platinum electrode that was modified by the deposition of the Gr-Au-Ag composites in the presence of various concentrations of carbamazepine. The experimental EIS records were used for the generation of an equivalent electrical circuit, based on the charge-transfer resistance (Rct), Warburg impedance (ZD), solution resistance (Rs), and a constant phase element (CPE) that characterizes the non-ideal interface capacitive responses.