We study the problem of designing dynamic intervention policies for minimizing networked defaults in financial networks. Formally, we consider a dynamic version of the celebrated Eisenberg-Noe model of financial network liabilities and use this to study the design of external intervention policies. Our controller has a fixed resource budget in each round and can use this to minimize the effect of demand/supply shocks in the network. We formulate the optimal intervention problem as a Markov Decision Process and show how we can leverage the problem structure to efficiently compute optimal intervention policies with continuous interventions and provide approximation algorithms for discrete interventions. Going beyond financial networks, we argue that our model captures dynamic network intervention in a much broader class of dynamic demand/supply settings with networked inter-dependencies. To demonstrate this, we apply our intervention algorithms to various application domains, including ridesharing, online transaction platforms, and financial networks with agent mobility. In each case, we study the relationship between node centrality and intervention strength, as well as the fairness properties of the optimal interventions.