Energy-efficiency (EE) is critical for device-to-device (D2D) enabled cellular networks due to limited battery capacity and severe cochannel interference. In this paper, we address the EE optimization problem by adopting a stable matching approach. The NP-hard joint resource allocation problem is formulated as a one-to-one matching problem under two-sided preferences, which vary dynamically with channel states and interference levels. A game-theoretic approach is employed to analyze the interactions and correlations among user equipments (UEs), and an iterative power allocation algorithm is developed to establish mutual preferences based on nonlinear fractional programing. We then employ the Gale-Shapley algorithm to match D2D pairs with cellular UEs, which is proved to be stable and weak Pareto optimal. We provide a theoretical analysis and description for implementation details and algorithmic complexity. We also extend the algorithm to address scalability issues in large-scale networks by developing tie-breaking and preference-deletion-based matching rules. Simulation results validate the theoretical analysis and demonstrate that significant performance gains of average EE and matching satisfactions can be achieved by the proposed algorithm.