Karst landforms cover 7%–12% of the Earth’s continental area and provide water resources for 25% of the global population. Climate, particularly frequent climate extremes, may greatly affect the annual runoff, especially in climate-sensitive regions such as a karst area of southwest China. Knowledge of the linkage between climate and runoff is urgently needed for smart water resources management. This study therefore selected five catchments that have different carbonized rock coverage (from 11% to 64%) to detect the dominant climatic variables driving changes in annual runoff for the period of 1957–2011 in southwest China. Because climatic variables are highly codependent, a partial least squares regression (PLSR) was used to elucidate the linkages between runoff and 17 climatic variables. Results indicated that the dominant climatic factors driving annual runoff are annual total precipitation, rainy days, heavy precipitation amount, heavy precipitation days, rainstorm amount, and rainstorm days. These six factors are generally used to represent extreme climatic events, and hence it may demonstrate that annual runoff is highly linked to precipitation extremes in this region. The PLSR approach presented in this study is beneficial and novel, as it enables the elimination of codependency among the variables and facilitates a more unbiased view of the contribution of the changes in climatic variables to the changes in runoff. As a practical and simple tool, the PLSR approach is thus recommended for application to a variety of other catchments.