The paper describes the development of a carbon veil-based electrode (CVE) for determining uric acid (UA) in saliva. The electrode was manufactured by lamination technology, electrochemically activated and used as a highly sensitive voltammetric sensor (CVEact). Potentiostatic polarization of the electrode at 2.0 V in H2SO4 solution resulted in a higher number of oxygen and nitrogen-containing groups on the electrode surface; lower charge transfer resistance; a 1.5 times increase in the effective surface area and a decrease in the UA oxidation potential by over 0.4 V, compared with the non-activated CVE, which was confirmed by energy dispersive X-ray spectroscopy, electrochemical impedance spectroscopy, chronoamperometry and linear sweep voltammetry. The developed sensor is characterized by a low detection limit of 0.05 µM and a wide linear range (0.09–700 µM). The results suggest that the sensor has perspective applications for quick determination of UA in artificial and human saliva. RSD does not exceed 3.9%, and recovery is 96–105%. UA makes a significant contribution to the antioxidant activity (AOA) of saliva (≈60%). In addition to its high analytical characteristics, the important advantages of the proposed CVEact are the simple, scalable, and cost-effective manufacturing technology and the absence of additional complex and time-consuming modification operations.