Extreme weather events, many of which are climate change related, are occurring with increasing frequency and intensity and causing catastrophic outages, reminding the need to enhance the resilience of power systems. This paper proposes a proactive operation strategy to enhance system resilience during an unfolding extreme event. The uncertain sequential transition of system states driven by the evolution of extreme events is modeled as a Markov process. At each decision epoch, the system topology is used to construct a Markov state. Transition probabilities are evaluated according to failure rates caused by extreme events. For each state, a recursive value function, including a current cost and a future cost, is established with operation constraints and intertemporal constraints. An optimal strategy is established by optimizing the recursive model, which is transformed into a mixed integer linear programming by using the linear scalarization method, with the probability of each state as the weight of each objective. The IEEE 30-bus system, the IEEE 118-bus system, and a realistic provincial power grid are used to validate the proposed method. The results demonstrate that the proposed proactive operation strategies can reduce the loss of load due to the development of extreme events.