Managing the performance at the flow level through traffic measurement is crucial for effective network management. With the rapid rise in link speeds, collecting all packets has become difficult, so packet sampling has been attracting attention as a scalable means of measuring flow statistics. In this paper, we firstly propose a method of estimating TCP flow rates of sampled flows through packet sampling, and then develop a method of detecting performance degradation at the TCP flow level from the estimated flow rates. In the method of estimating flow rates, we use sequence numbers of sampled packets, which make it possible to improve markedly the accuracy of estimating the flow rates of sampled flows. Using both an analytical model and measurement data, we show that this method gives accurate estimations. We also show that, by observing the estimated rates of sampled flows, we can detect TCP performance degradation. The method of detecting performance degradation is based on the following two findings: (i) sampled flows tend to have high flow-rates and (ii) when a link becomes congested, the performance of high-rate flows becomes degraded first. These characteristics indicate that sampled flows are sensitive to congestion, so we can detect performance degradation of flows that are sensitive to congestion by observing the rate of sampled flows. We also show the effectiveness of our method using measurement data.