In one embodiment, a method comprises: receiving, by a constrained wireless network device comprising a local clock, a plurality of messages from respective neighboring wireless network devices advertising as available parent devices in a directed acyclic graph of a time-synchronized network that is synchronized to a master clock device; determining, by the constrained wireless network device, a corresponding timing error of the local clock relative to each message output by the corresponding available parent device; and executing, by the constrained wireless network device, a distributed time synchronization of the local clock with the master clock device based on correlating the respective timing errors relative to the local clock.