Modern high-performance computing (HPC) systems concurrently execute multiple distributed applications that contend for the high-speed network leading to congestion. Consequently, application runtime variability and suboptimal system utilization are observed in production systems. To address these problems, we propose Netscope, a congestion mitigation framework based on a novel delay sensitivity metric that quantifies the impact of congestion on application runtime. Netscope uses delay sensitivity estimates to drive a congestion mitigation mechanism to selectively throttle applications that are less susceptible to congestion. We evaluate Netscope on two Cray Aries systems, including a production supercomputer, on common scientific applications. Our evaluation shows that Netscope has a low training cost and accurately estimates the impact of congestion on application runtime with a correlation between 0.7 and 0.9. Moreover, Netscope reduces application tail runtime increase by up to 16.3× while improving the median system utility by 12%.