The inferior electrical contact to two-dimensional (2D) materials is a critical challenge for their application in post-silicon very large- scale integrated circuits. Electrical contacts were generally related to their resistive effect, quantified as contact resistance. With a systematic investigation, this work demonstrates a capacitive metal-insulator-semiconductor (MIS) field-effect at the electrical contacts to 2D materials: The field-effect depletes or accumulates charge carriers, redistributes the voltage potential, and gives rise to abnormal current saturation and nonlinearity. On one hand, the current saturation hinders the devices' driving ability, which can be eliminated with carefully engineered contact configurations. On the other hand, by introducing the nonlinearity to monolithic analog artificial neural network circuits, the circuits' perception ability can be significantly enhanced, as evidenced using a coronavirus disease 2019 (COVID-19) critical illness prediction model. This work provides a comprehension of the field-effect at the electrical contacts to 2D materials, which is fundamental to the design, simulation, and fabrication of electronics based on 2D materials.