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MQTT is an application-layer protocol that eventually became popular in the Internet of Things (IoT) and Industrial IoT (IIoT) thanks to its simplicity and effective publisher-subscriber messaging model that enables its use in embedded resource-constrained devices. However, MQTT features a limited set of Quality-of-Service classes addressing exclusively message delivery, impairing its use in IIoT applications subject to timeliness requirements. This limitation of MQTT has been addressed in the literature, but with focus on the broker real-time operation, only. This paper adds to the state-of-the-art, by proposing a set of extensions to the MQTT protocol grounded on Software-Defined Networking (SDN) that enable, at the network level, attaining real-time communication services. Simulation results validate the benefits of the proposed extensions.This work is funded by the FCT/MCTES through national funds and, when applicable, co-funded by community funds under the projects UIDB/50008/2020-UIDP/50008/2020 and UIDB/04234/2020. It is also supported by Portuguese National Funds through FCT scholarship PD/BD/137388/2018.