In the wake of an increasing number in targeted and complex attacks on enterprise networks, there is a growing need for timely, efficient and strategic network response. Intrusion detection systems provide network administrators with a plethora of monitoring information, but that information must often be processed manually to enable decisions on response actions and thwart attacks. This gap between detection time and response time, which may be months long, may allow attackers to move freely in the network and achieve their goals. In this paper, we present a game-theoretic approach for automatic network response to an attacker that is moving laterally in an enterprise network. To do so, we first model the system as a network services graph and use monitoring information to label the graph with possible attacker lateral movement communications. We then build a defense-based zero-sum game in which we aim to prevent the attacker from reaching a sensitive node in the network. Solving the matrix game for saddle-point strategies provides us with an effective way to select appropriate response actions. We use simulations to show that our engine can efficiently delay an attacker that is moving laterally in the network from reaching the sensitive target, thus giving network administrators enough time to analyze the monitoring data and deploy effective actions to neutralize any impending threats.