The scale of electric vehicles (EVs) in microgrids is growing prominently. However, the stochasticity of EV charging behavior poses formidable obstacles to exploring their dispatch potential. To solve this issue, an optimization strategy for EV-integrated microgrids considering peer-to-peer (P2P) transactions has been proposed in this paper. This research strategy contributes to the sustainable development of microgrids under large-scale EV integration. Firstly, a novel cooperative operation framework considering P2P transactions is established, in which the impact factors of EV charging are regarded to simulate its stochasticity and the energy trading process of the EV-integrated microgrid participating in P2P transactions is defined. Secondly, cost models for the EV-integrated microgrid are established. Thirdly, a three-stage optimization strategy is proposed to simplify the solving process. It transforms the scheduling problem into three solvable subproblems and restructures them with Lagrangian relaxation. Finally, case studies demonstrate that the proposed strategy optimizes EV load distribution, reduces the overall operational cost of the EV-integrated microgrid, and enhances the economic efficiency of each microgrid participating in P2P transactions.