Background: This study investigates the psychophysiological stress profiles of professional basketball players by simultaneously analyzing two distinct neuroendocrine pathways: the sympathetic–adrenal–medullary (SAM) system, via salivary alpha-amylase (AA), and the hypothalamic–pituitary–adrenal (HPA) axis, via salivary cortisol (C). While competitive environments are known to elicit significant stress, the interaction between game-specific variables—such as playing time (PT) and tactical position—and those biomarkers remains insufficiently explored in real-time, official match settings. Methods: Twelve professional male basketball players were monitored across four official matches. Salivary samples were collected, and stress biomarkers (AA and C) were analyzed at three timepoints: pre-match, half-time, and post-match. Results: Results indicate that stress responses are non-uniform and highly context-dependent. A significant spike in AA was observed during the first match (p < 0.001; ES = 0.82; 95% CI −0.01–1.66), where concentrations rose from a pre-match mean of 247.9 ± 232.59 U/mL to a post-match peak of 674.39 ± 693.33 U/mL. Cortisol responses did not vary significantly across matches but exhibited a strong positive correlation with PT (p = 0.01; R = 0.76), identifying that C may serve as a primary marker of individual physical workload. Positional analysis revealed significant divergence in HPA activation; guards (0.55 ± 0.31 µg/dL) and centers (0.51 ± 0.22 µg/dL) exhibited higher cortisol levels compared to forwards (0.24 ± 0.18 µg/dL), reflecting the high cognitive/decision-making load of guards and the mechanical/physical contact load of centers. Conclusions: The observed differences in AA and C liberation suggest that stress responses during matches are influenced by a complex interaction of physiological and psychological stimuli characteristic of competitive basketball. Consequently, these findings indicate the importance and value of a dual-biomarker approach which might provide a framework for optimized training load management and recovery protocols in elite basketball.