The disclosure herein describes a system, which provides uniform access to a gateway in an extended virtualized layer-2 network. During operation, the system identifies a media access control (MAC) address, which is associated with a respective gateway in the extended virtualized layer-2 network, in a layer-2 header of a data frame. This MAC address is specific to the extended virtualized layer-2 network (e.g., for a different extended virtualized layer-2 network, a different MAC address is associated with a respective gateway). The system modifies the layer-2 header by swapping the MAC address with another MAC address, which uniquely identifies a gateway in the extended virtualized layer-2 network, in the layer-2 header and forwards the frame with the modified header to the gateway.