Serious soil and water loss affects the economy and the living quality of the population in faulted basins. Since 2002, China has carried out large-scale ecological restoration projects in karst areas. However, the karst faulted basins have experienced complex climatic changes, which makes it difficult to assess the ecological restoration effects quantitatively. Using the improved Budyko model, basin factor (n) and sediment content factor (C) were divided into climate influence and ecological restoration influence by second-order approximation, and the change ratio of climate influence and ecological restoration on sediment yield and loss was quantitatively calculated in the representative basin of the Nandong Underground River System (NURS). This was carried out in order to effectively distinguish the effects of climate change and ecological restoration on runoff and sediment change in the NURS. Furthermore, this study sought to understand the mechanism of runoff and sediment change and to evaluate the ecological restoration in the faulted basin to provide a scientific basis for the next stage of soil and water conservation policy formulation. The results showed that: (1) Using Pettitt to test the abrupt change of water and sediment in the NURS from 1987 to 2018, we found that 2002 was the abrupt change year of water and sediment in the basin. Before and after the mutation, the runoff and sediment yield decreased significantly, with the change rates of −15.5% and −51.8%, respectively. The decrease in precipitation and the increase in E0 were not significant, which were −4.5% and 1.4% respectively. (2) By calculating the correlation coefficient and the double logarithm function, it was found that the maximum temperature is the main climatic factor affecting the underlying surface factor n, and precipitation is the main climatic factor affecting the sediment concentration c. (3) Climate change reduced runoff by 77.6%. Ecological restoration has reduced sediment by 51.3 percent. The sensitivity of runoff to maximum temperature was 3.61. The sensitivity of grain yield to precipitation and NDVI was 5.37 and 3.26, respectively. The results show that climate is the main factor of runoff reduction, and ecological restoration is the main factor of sediment reduction. Ecological restoration has greatly reduced sediment production, and ecological engineering has made remarkable progress. However, the reduction of runoff caused by climate change should be paid more attention. The results of these studies will help to better formulate land use management policies for soil and water conservation.