With the recent explosive growth in online classes and virtual meetings, real-time video communication has quickly become an essential tool to everyone. Despite its widespread deployment, our investigation revealed that current protocols, ranging from industry standards such as WebRTC, to state-of-the-art research such as Salsify, often perform sub-optimally in the presence of competing flows sharing the same bottleneck. For example, WebRTC's throughput can degrade from 73% to a mere 8% of the available bandwidth when competing with just two TCP flows. We tackle this problem in this work by developing a novel PIPES protocol designed for real-time video applications in the presence of competing TCP traffic. PIPES employs a new inband bandwidth estimation method that can quickly and accurately measure the bottleneck link bandwidth even with competing flows. Moreover, PIPES can detect the absence or presence of competing flows which enables it to maximize video quality when there is no competing flow, and to maintain acceptable video quality while sharing bandwidth with competing flows. Experiments demonstrate that PIPES achieves throughput and delay comparable to the state-of-art protocols, but outperforms them significantly in the presence of competing TCP flows.