In the coming years, the dominance of video in global Internet traffic is expected to intensify due to the ongoing migration from analog CCTV to IP-based surveillance systems. As opposed to analog, IP cameras can be integrated into pre-existing computer networks and thus, are more cost-effective. However, since video is bandwidth-intensive, contention among the streams from multiple IP cameras and traffic from other applications results to a severely degraded network performance. Software-Defined Networking (SDN) is a relatively new paradigm which aims to build dynamically configurable networks. The decoupling of forwarding and control functions in SDN architecture enables a centralized controller to create a map of the network topology by utilizing the information collected from the switches. This paper proposes an SDN-based framework to enhance the performance of IP Video Surveillance (IPVS) systems deployed over underprovisioned networks. As a means of allowing the controller to infer a stream's QoS metrics and to execute bitrate adjustment or rerouting as necessary, two video quality indicators were also formulated by utilizing the statistics messages available in OpenFlow, a widely recognized protocol in SDN. Moreover, our design is built on the idea that the video streams in surveillance systems offer different utilities depending on the captured event. Experimental results show that employing the proposed framework improved the video streams' overall packet loss, latency, jitter and throughput by 88%, 36%, 11% and 5% respectively. The comparison of the video streams' QoS metrics also suggests that the framework is capable of prioritizing the reception of selected streams. Furthermore, we also demonstrate that the proposed framework can be easily extended to handle the case of an IPVS system wherein the streams are subjected to dynamic priority assignment.