The present study describes the electrochemical properties of three screen-printed electrodes (SPEs), the first electrode being carbon-based (C), the second graphene-based (GPH), and the third based on GPH modified with gold nanoparticles (GNP). These electrodes were used for the study of the electrochemical behavior of chlorogenic acid in different aqueous solutions, at pH = 7. In chlorogenic acid solution, a redox process was noticed in the case of all three electrodes; GPH and GNP significantly improved the sensor response regarding sensitivity and reversibility, a fact demonstrated by characterizing the sensor by cyclic voltammetry in potassium ferrocyanide, which corresponds to the exchange of two electrons and two protons. Moreover, the calibration curves for each sensor were developed, subsequently calculating the detection limits (LOD) and the quantification limits (LOQ). Low LOD and LOQ were obtained, the best—of the order of 10−7 M (LOD = 0.62 × 10−7 M; LOQ = 1.97 × 10−7 M)—being obtained in the case of GPH-GNP-SPE, which demonstrates that the method may be applied for determining chlorogenic acid in real samples. Thus, the sensors were successfully used for the quantitative determination of chlorogenic acid in three nutraceutical products. The validation of the results was done using the FTIR method. The results obtained by cyclic voltammetry were in accordance with those obtained by the spectrometric method, without significant differences from a statistical point of view.