This paper studies a continuous-review stochastic inventory problem for a firm facing random demand and random supply disruptions. The supplier experiences operational (on) and disrupted (off) periods with exponentially distributed durations. The firm adopts an order-up-to level policy during the on period and additionally can release an emergency order based on the inventory level just before disruption. This inventory policy is described by a continuous-time Markov chain model. We analyze the model for two different lead time scenarios and suggest solution approaches yielding the optimal policy parameters. In a numerical study, we explore the value of exercising such a policy and show that an emergency ordering opportunity at the disruption time brings substantial cost savings in cases with high lost sales cost, long off period, and low percentage of supplier's availability.