The software defined wide area network (SD-WAN) architecture is continuously improving to meet the diverse customer needs of different sectors. Traffic-tunneling over a certain uplink is a core part of SD-WAN’s security feature to route desired application traffic over an uplink that caters quality of service (QoS) as per service level agreement (SLA). However, the classified controlled traffic of tunnel health probing protocol (THPP) active on each pair of tunnel end-points contends with mainstream traffic in the event of network congestion impacting the QoS of high priority classified traffic such as an audio-video (AV) stream of critical importance. This may further lead to packet loss, increased latency, and jitter for both THPP and mainstream traffic. The available uplink bandwidth is a critical network resource that affects the configured behavior of a standard queuing discipline (Qdisc), resulting in formidable challenges such as buffer overflow, priority inversion, increased latency, and ineffective rate-limiting. This work initially investigates and demonstrates the shortcomings faced by standard Qdiscs during network congestion and their impact on transmission of mainstream real-time data in the presence of THPP traffic in a custom emulated SD-WAN environment. Next, a novel enhanced flow rate algorithm (EFR) is systematically developed for superior Qdisc configuration and uplink utilization in SD-WANs during network congestion. Exhaustive simulation results demonstrate that the proposed EFR-based Qdisc significantly reduces contention to the mainstream traffic during congestion along with an efficient uplink bandwidth distribution among THPP, mainstream and best-effort traffic (BE).