We characterize the degrees-of-freedom (DoF) region of a class of two-unicast wireless networks under the assumption of delayed channel state information at the transmitters. We consider a layered topology with arbitrary connectivity, and we introduce new outer-bounds on the DoF region through the graph-theoretic notion of bottleneck nodes. Such nodes act as informational bottlenecks only under the assumption of delayed channel state information. Combining our outer-bounds with new achievability schemes, we characterize the DoF region of two-unicast wireless networks with informational bottlenecks. We show that unlike the instantaneous channel state information model, the sum DoF of two-unicast networks with delayed channel knowledge can take an infinite set of values. We compare our results to the best previously known outer-bounds, and we show that the gap can be arbitrary large in favor of the current work.