In this paper, we aim to secure the D2D communication of the D2D-underlaid cellular network by leveraging covert communication to hide its presence from the vigilant adversary. In particular, there are adversaries aiming to detect D2D communications based on their received signal powers. To avoid being detected, the legitimate entity, i.e., D2D-underlaid cellular network, performs power control so as to hide the presence of the D2D communication. We model the combat between the adversaries and the legitimate entity as a two-stage Stackelberg game. Therein, the adversaries are the followers and aim to minimize their detection errors at the lower stage while the legitimate entity is the leader and aims to maximize its utility constrained by the D2D communication covertness and the cellular quality of service (QoS) at the upper stage. Different from the conventional works, the study of the combat is conducted from the system-level perspective, where the scenario that a large-scale D2D-underlaid cellular network threatened by massive spatially distributed adversaries is considered and the network spatial configuration is modeled by stochastic geometry. We obtain the adversary's optimal strategy as the best response from the lower stage and also both analytically and numerically verify its optimality. Taking into account the best response from the lower stage, we design a bi-level algorithm based on the successive convex approximation (SCA) method to search for the optimal strategy of the legitimate entity, which together with the best response from the lower stage constitute the Stackelberg equilibrium. Numerical results are presented to evaluate the network performance and reveal practical insights that instead of improving the legitimate utility by strengthening the D2D link reliability, increasing D2D transmission power will degrade it due to the security concern.