We propose CentRoute a centralized on-demand tree-based routing protocol for resource constrained wireless sensor networks. CentRoute is a unicast routing protocol that utilizes source routing to form paths from a node to the sink and vice-versa. Each node in the network can connect to a single tree at a time which is controlled by a dynamically selected root (or sink). By centralizing routing decisions at the root of the tree, which is not subject to the same resource constraints as the rest of the nodes, CentRoute can avoid routing instabilities and inconsistencies, such as loops. The protocol has constant state requirements on the resource-constrained nodes and as a result can scale to networks of high density. Its on-demand nature results in a low control overhead, as the paths are maintained only when data flows through them. We evaluate the performance of our protocol using simulations as well as an experimental testbed.