A network device may generate a route advertisement that includes a media access control (MAC) address. The MAC address may correspond to a data link established between the network device and a customer edge (CE) device. The network device and the CE device may be associated with an Ethernet virtual private network (EVPN) that includes other network devices that are remote from the CE device. The network device may cause the route advertisement to be outputted over the EVPN. The route advertisement may permit the other network devices to learn that the data link is directly reachable via the MAC address, and may permit the other network devices, when configured as maintenance endpoints (MEPs), to directly address performance monitoring-related unicast packets, intended for the data link, using the MAC address, such that flooding of the performance monitoring-related unicast packets is avoided.