MQTT is one of the most popular application-layer protocols used in the scope of the Internet-of-Things (IoT) and Industrial-Internet-of-Things (IIoT), given its suitability for resource-constrained embedded systems. However, MQTT Quality-of-Service policies do not support timeliness requirements, which is common in IIoT. The literature reports several research works that address this limitation, but they are limited in scope (e.g., improvements in the broker's internal operation, control of the publisher's data rate, and path optimizations). Conversely, this paper presents a comprehensive architectural approach, proposing a set of extensions to the MQTT protocol that allow applications to explicitly specify real-time requirements and instantiate corresponding network reservations to enforce the desired temporal behavior. Such reservations are enforced via Software Defined Networking, specifically the OpenFlow protocol, but other protocols that allow bandwidth reservations, e.g., TSN, can also be used. This paper presents the proposed system architecture together with extensive emulation and implementation results that validate the feasibility of the approach, showing that time-sensitive MQTT traffic can be effectively segregated and prioritized to meet application-defined real-time requirements. Using several combinations of network topologies and load levels and comparing to the absence of the proposed real-time mechanisms, both average and worst-case latencies of the time-sensitive traffic decreased to approximately half, while for the normal traffic, they increased by approximately 10%.