Observed streamflow of headwater catchments of the Tarim River (Central Asia) increased by about 30% over the period 1957–2004. This study aims at assessing to which extent these streamflow trends can be attributed to changes in air temperature or precipitation. The analysis includes a data-based approach using multiple linear regression and a simulation-based approach using a hydrological model. The hydrological model considers changes in both glacier area and surface elevation. It was calibrated using a multiobjective optimization algorithm with calibration criteria based on glacier mass balance and daily and interannual variations of discharge. The individual contributions to the overall streamflow trends from changes in glacier geometry, temperature, and precipitation were assessed using simulation experiments with a constant glacier geometry and with detrended temperature and precipitation time series. The results showed that the observed changes in streamflow were consistent with the changes in temperature and precipitation. In the Sari-Djaz catchment, increasing temperatures and related increase of glacier melt were identified as the dominant driver, while in the Kakshaal catchment, both increasing temperatures and increasing precipitation played a major role. Comparing the two approaches, an advantage of the simulation-based approach is the fact that it is based on process-based relationships implemented in the hydrological model instead of statistical links in the regression model. However, data-based approaches are less affected by model parameter and structural uncertainties and typically fast to apply. A complementary application of both approaches is recommended.