With the intensification of human activities and climate variability, balancing ecosystem service (ES) supply and demand is critical for regional sustainable development. Existing studies predominantly focus on linear driving effects and lack integrated quantitative frameworks that link the spatiotemporal dynamics of ES supply–demand relationships (ESSDRs) with their nonlinear driving mechanisms, and few have systematically quantified the critical thresholds of driving factors and their interactive effects. To address these research gaps, this study quantified the supply, demand, and supply–demand ratios of four key ESs (food production [FP], carbon sequestration [CS], water yield [WY], and soil retention [SR]) in the Yellow River Basin of Henan Province (2000–2020) using the InVEST model and multi-source data. An analytical framework integrating the Extreme Gradient Boosting (XGBoost) model and Shapley Additive Explanations (SHAP) was established to identify dominant drivers, reveal nonlinear response patterns, and quantify critical thresholds. The results showed that FP and CS supply increased continuously, while WY and SR supply slightly declined; CS and WY demand grew faster than supply, leading to expanding deficits, whereas FP and SR maintained relative balance. Spatially, FP/CS surpluses concentrated in eastern plains and southwestern forests, WY deficits occurred in the northwest, and SR balance prevailed in most regions. Dominant drivers differed by ES type—arable land proportion (FP), population density (CS), precipitation (WY), and slope (SR)—all exhibiting distinct threshold effects (e.g., arable land proportion >0.6, slope >3°). These findings provide novel insights into ESSDR spatial heterogeneity and threshold-based regulation, offering a scientific basis for differentiated ecological management and sustainable spatial planning in the Yellow River Basin and similar ecologically vulnerable regions.