Net ecosystem productivity (NEP) represents a key indicator of terrestrial carbon sink strength and its response to hydroclimatic variability in dryland regions. However, basin-scale evidence on the long-term dynamics, persistence, and hydroclimatic regulation of NEP remains limited in the Yellow River Basin (YRB) under concurrent warming, drying, and rapid land-use change. Here, we generated an annual 1-km NEP dataset for 2001-2024 by integrating MODIS-based NPP with a regionally calibrated CASA framework and an evapotranspiration-constrained empirical heterotrophic respiration scheme. Temporal trends and persistence were quantified using Theil-Sen, Mann-Kendall, and Hurst analyses. Hydroclimatic controls were investigated using a random forest model interpreted with SHAP, incorporating predictors of water availability, atmospheric dryness, temperature, radiation, and drought conditions. Results show a modest increase in basin-mean NEP but strong spatial heterogeneity. Persistent carbon sinks were concentrated in the semi-humid southeastern YRB, whereas sustained declines occurred in water-limited and rapidly urbanizing regions. Trend-persistence coupling suggests that current improvement areas are likely to maintain their carbon sink function, while extensive regions may continue long-term degradation. Water availability was the dominant control, with saturation occurring at similar to 600 mm annual precipitation and 30-40% relative soil moisture. Atmospheric dryness strongly constrained NEP when vapor pressure deficit exceeded similar to 0.6 kPa, whereas temperature and radiation enhanced NEP mainly under weak moisture limitation. These results highlight that the stability of terrestrial carbon sinks in this large dryland basin is governed by interacting hydroclimatic constraints. The identified spatial patterns and process-based thresholds improve understanding of carbon-water coupling and provide scientific support for climate-adaptive carbon sink management in dryland river basins.