Cross-border power cooperation is considered a pathway for optimal regional use of renewable resources and the reduction of carbon emissions. To enhance such cooperation, it is essential to understand the game behaviors of the involved parties. This study applied evolutionary game theory (EGT) and system dynamics (SD) methods to analyze the factors influencing strategic choices and cooperation benefits in the China–Laos electricity cooperation. An EGT model was first developed to examine the interactive behavior of both parties and the stability of strategies. Subsequently, an SD model of EGT was constructed to simulate the evolutionary game process, explore the intrinsic mechanisms of the evolutionary game, and analyze the factors affecting strategy selection. The results show that: (1) the gaming behaviors cannot be ignored in cross-border power cooperation; (2) compared to the cross-border trade scenario, the strategic cooperation will generate more benefits for the parties involved and thus will be selected as the cooperation game evolves; (3) the initial strategy ratio of both parties is crucial, influencing the direction of strategy evolution and the time to reach equilibrium; (4) the choice of system cooperation strategy is affected by the unit profit of electricity trade, input cost, incremental return, trade volume, transaction cost, excess return, fine for agreement violation, and the ratio of benefit allocation, among which the former three are critical.