We consider the problem of throughput-optimal broadcast- ing in time-varying wireless networks, whose underlying topology is restricted to Directed Acyclic Graphs (DAG). Previous broadcast algorithms route packets along spanning trees. In large networks with time-varying connectivities, these trees are difficult to compute and maintain. In this paper we propose a new online throughput-optimal broadcast algorithm which makes packet-by-packet scheduling and routing decisions, obviating the need for maintaining any global topological structures, such as spanning-trees. Our algorithm relies on system-state information for making transmission decisions and hence, may be thought of as a generalization of the well-known back-pressure algorithm which makes point-to-point unicast transmission decisions based on queue-length information, without requiring knowledge of end-to-end paths. Technically, the back-pressure algorithm is derived by stochastically stabilizing the network-queues. However, because of packet-duplications associated with broadcast, the work-conservation principle is violated and queuing processes are difficult to define in the broadcast problem. To address this fundamental issue, we identify certain state-variables which behave like virtual queues in the broadcast setting. By stochastically stabilizing these virtual queues, we devise a throughput-optimal broadcast policy. We also derive new characterizations of the broadcast-capacity of time-varying wireless DAGs and derive an efficient algorithm to compute the capacity exactly under certain assumptions of interference model, and a poly-time approximation algorithm for computing the capacity under less restrictive assumptions.